Answer to Q116
How many people is "two pairs of twins twice"?
A twin is one person (that is, one of the two persons born at the same time).
Twins are the two persons born at the same time and same is pair of twins. Pair of twins or set of twins (actually pair of twins is more commonly used) are 2 people.
Two pairs of twins is then 2 x 2 which is 4.
Twice is then 2 x 4 which is 8.
Answer: 8
How many people is "two pairs of twins twice"?
A twin is one person (that is, one of the two persons born at the same time).
Twins are the two persons born at the same time and same is pair of twins. Pair of twins or set of twins (actually pair of twins is more commonly used) are 2 people.
Two pairs of twins is then 2 x 2 which is 4.
Twice is then 2 x 4 which is 8.
Answer: 8
Answer to Q117
A pencil with a pentagonal cross section has the maker's logo imprinted on one of its five faces. If the pencil is rolled on the table, what is the probability that it stops with the logo facing directly up?
Above is the diagram of a pencil with a pentagonal cross section. When you roll the pencil, it will always stop on it flat side with the corner point up. The makers logo will never be pointing DIRECTLY up.
Probability of the makers logo pointing directly up is therefore zero.
Answer: 0%
A pencil with a pentagonal cross section has the maker's logo imprinted on one of its five faces. If the pencil is rolled on the table, what is the probability that it stops with the logo facing directly up?
Above is the diagram of a pencil with a pentagonal cross section. When you roll the pencil, it will always stop on it flat side with the corner point up. The makers logo will never be pointing DIRECTLY up.
Probability of the makers logo pointing directly up is therefore zero.
Answer: 0%
Answer to Q118
A visitor points to a portrait on the wall and asks who it is. "Brothers and sisters have I none" says the host, "but that man's father is my father's son".
Who is in the picture?
Let start with "Brothers and sisters have I none", this simply means the host does not have any brother or sister. Agreed?
Then he said "my father's son", but remember he does not have any brother and sister, so he's father son is basically him, you agree with that? Good! So we can replace "my father's son" with "me" in that statement.
"Brothers and sisters have I none, but that man's father is me".
But the first phrase "Brothers and sisters have I none," has served it purpose so we can remove it, the statement becomes:
"but that man's father is me" simplified, it becomes "That man's father is me"
"That man's father is me"
Obviously, he is talking about his own son.
Answer: The Host's Son
A visitor points to a portrait on the wall and asks who it is. "Brothers and sisters have I none" says the host, "but that man's father is my father's son".
Who is in the picture?
Let start with "Brothers and sisters have I none", this simply means the host does not have any brother or sister. Agreed?
Then he said "my father's son", but remember he does not have any brother and sister, so he's father son is basically him, you agree with that? Good! So we can replace "my father's son" with "me" in that statement.
"Brothers and sisters have I none, but that man's father is me".
But the first phrase "Brothers and sisters have I none," has served it purpose so we can remove it, the statement becomes:
"but that man's father is me" simplified, it becomes "That man's father is me"
"That man's father is me"
Obviously, he is talking about his own son.
Answer: The Host's Son
Answer to Q119
One bottle contains 100 liters of wine, another 100 liters of water. Ten liters of wine is moved from the wine bottle to the water bottle and properly mixed in. Ten liters of the mixture is then moved from the water bottle to the wine bottle.
Which of the below statement is correct?
Wine bottle = 100 liters
Water bottle = 100 liters
Ten liters of wine is moved from the wine bottle to the water bottle and properly mixed in.
Now,
Wine bottle is 90 liters
Water bottle is 110 liters
But water bottle contains 100 liters of water and 10 liters of wine. That is ratio 100:10 which is same as 10:1
Ten liters of the mixture is then moved from the water bottle to the wine bottle.
10 liters of the mixture at ratio 10:1 will contain the following
Water = (10 ÷ 11) x 10 liters = 9.09 liters
Wine = (1 ÷ 11) x 10 liters = 0.91 liters
What's now in the wine bottle?
Wine bottle previously had 90 liters of wine.
Then mixture of 0.91 liters of wine and 9.09 liters water was added to it
So it now has 90 + 0.91 = 90.91 liters of wine
What's now in the water bottle?
Water bottle previously had 110 liters of mixture which was 100 liters of water and 10 liters of wine.
Then mixture of 0.91 liters of wine and 9.09 liters water was removed from it.
So it now has 100 - 9.09 = 90.91 liters of water
So, we have 90.91 liters of wine in the wine bottle and 90.91 liters of water in the water bottle.
Answer: There are the same amount of water in the water bottle as wine in the wine bottle!
One bottle contains 100 liters of wine, another 100 liters of water. Ten liters of wine is moved from the wine bottle to the water bottle and properly mixed in. Ten liters of the mixture is then moved from the water bottle to the wine bottle.
Which of the below statement is correct?
Wine bottle = 100 liters
Water bottle = 100 liters
Ten liters of wine is moved from the wine bottle to the water bottle and properly mixed in.
Now,
Wine bottle is 90 liters
Water bottle is 110 liters
But water bottle contains 100 liters of water and 10 liters of wine. That is ratio 100:10 which is same as 10:1
Ten liters of the mixture is then moved from the water bottle to the wine bottle.
10 liters of the mixture at ratio 10:1 will contain the following
Water = (10 ÷ 11) x 10 liters = 9.09 liters
Wine = (1 ÷ 11) x 10 liters = 0.91 liters
What's now in the wine bottle?
Wine bottle previously had 90 liters of wine.
Then mixture of 0.91 liters of wine and 9.09 liters water was added to it
So it now has 90 + 0.91 = 90.91 liters of wine
What's now in the water bottle?
Water bottle previously had 110 liters of mixture which was 100 liters of water and 10 liters of wine.
Then mixture of 0.91 liters of wine and 9.09 liters water was removed from it.
So it now has 100 - 9.09 = 90.91 liters of water
So, we have 90.91 liters of wine in the wine bottle and 90.91 liters of water in the water bottle.
Answer: There are the same amount of water in the water bottle as wine in the wine bottle!
Answer to Q120
The three volumes of a book sit in chronical order on a shelf. Each is 1¼ inches thick, comprising an inch of pages and ⅛ inch for each cover. A bookworm bores from page 1, volume I, to the last page of volume III. How far does it travel?
Ok see the first diagram in the attached picture, do you agree? Putting a book on the shelf, the first page will be on your right and the last page on your left. Good!
Now the books were arranged in chronological order (second diagram). The bookworm bores from page 1 of volume I to last page of volume III. You will agree with me that the last page of Volume III will be the first page the bookworm encounters in Volume III (remember last page is on the left and first page is on the right).
So what we are to find is X (from the second diagram).
X becomes:
= One cover of Volume I + whole book of Volume II + one cover of Volume III
= ⅛ inches + 1¼ inches + ⅛ inches
= 1½ inches
Answer: 1½ inches
Pardon the freehand diagram, I am not a graphic designer 🙈
The three volumes of a book sit in chronical order on a shelf. Each is 1¼ inches thick, comprising an inch of pages and ⅛ inch for each cover. A bookworm bores from page 1, volume I, to the last page of volume III. How far does it travel?
Ok see the first diagram in the attached picture, do you agree? Putting a book on the shelf, the first page will be on your right and the last page on your left. Good!
Now the books were arranged in chronological order (second diagram). The bookworm bores from page 1 of volume I to last page of volume III. You will agree with me that the last page of Volume III will be the first page the bookworm encounters in Volume III (remember last page is on the left and first page is on the right).
So what we are to find is X (from the second diagram).
X becomes:
= One cover of Volume I + whole book of Volume II + one cover of Volume III
= ⅛ inches + 1¼ inches + ⅛ inches
= 1½ inches
Answer: 1½ inches
Pardon the freehand diagram, I am not a graphic designer 🙈
Answer to Q121
Two neon signs are turned on at the same time. One blinks every 12 seconds. The other blinks every 15 seconds. In how many seconds will they both blink at the same time?
The answer is simply the Lowest Common Multiples between the two number 12 and 15, which will be 2 x 2 x 3 x 5 = 60
Another way to prove this is that at 60 seconds, the 12 seconds sign would have blinked 60 ÷ 12 = 5 times while the 15 seconds sign would have blinked 60 ÷ 15 = 4 times.
Answer: 60 seconds
Two neon signs are turned on at the same time. One blinks every 12 seconds. The other blinks every 15 seconds. In how many seconds will they both blink at the same time?
The answer is simply the Lowest Common Multiples between the two number 12 and 15, which will be 2 x 2 x 3 x 5 = 60
Another way to prove this is that at 60 seconds, the 12 seconds sign would have blinked 60 ÷ 12 = 5 times while the 15 seconds sign would have blinked 60 ÷ 15 = 4 times.
Answer: 60 seconds
Answer to Q122
15xy ÷ 3y can be rewritten as?
We are asked to simplify the above equation.
15 ÷ 3 = 5, so we can rewrite as 5xy ÷ y
xy ÷ y = x, so it becomes 5x
Answer: 5x
15xy ÷ 3y can be rewritten as?
We are asked to simplify the above equation.
15 ÷ 3 = 5, so we can rewrite as 5xy ÷ y
xy ÷ y = x, so it becomes 5x
Answer: 5x
Answer to Q123
Solve for y where 0.5y – 1.1 = 4.9
0.5y – 1.1 = 4.9
0.5y = 4.9 + 1.1 (sign changes when you move across your the equal)
0.5y = 6
Divide all through by 0.5
y = 6 ÷ 0.5
y = 6 ÷ ½
This can be rewritten as
y = 6 x 2 [a ÷ 1/b = a x b]
y = 12
Answer: 12
Solve for y where 0.5y – 1.1 = 4.9
0.5y – 1.1 = 4.9
0.5y = 4.9 + 1.1 (sign changes when you move across your the equal)
0.5y = 6
Divide all through by 0.5
y = 6 ÷ 0.5
y = 6 ÷ ½
This can be rewritten as
y = 6 x 2 [a ÷ 1/b = a x b]
y = 12
Answer: 12
Answer to Q124
Nine men went to a restaurant. Eight of them spent $6 each for their meals and the ninth man spent $4 more than the average expenditure of all nine men. What is the average expenditure?
Average simply is the sum of a set of data divided by the quantity of the data.
We know what 8 men spent which is $6 each
Let what the ninth man spent be = Y
Let the average of what the nine men spent be = Z
the ninth man spent $4 more than the average expenditure of all nine men
So, Y = Z + 4 (eqn 1)
average of what all nine men spent will then be
((6 x 8) + Y) ÷ 9 = Z
(48 + Y) ÷ 9 = Z
Multiply all through by 9
48 + Y = 9Z (eqn 2)
Put eqn 1 into eqn 2
48 + Z + 4 = 9Z
52 + Z = 9Z
52 = 9Z - Z
52 = 8Z
Z = 52 ÷ 8
Z = 6.5
So, average of the expenditure is $6.5
Answer: $6.5
Nine men went to a restaurant. Eight of them spent $6 each for their meals and the ninth man spent $4 more than the average expenditure of all nine men. What is the average expenditure?
Average simply is the sum of a set of data divided by the quantity of the data.
We know what 8 men spent which is $6 each
Let what the ninth man spent be = Y
Let the average of what the nine men spent be = Z
the ninth man spent $4 more than the average expenditure of all nine men
So, Y = Z + 4 (eqn 1)
average of what all nine men spent will then be
((6 x 8) + Y) ÷ 9 = Z
(48 + Y) ÷ 9 = Z
Multiply all through by 9
48 + Y = 9Z (eqn 2)
Put eqn 1 into eqn 2
48 + Z + 4 = 9Z
52 + Z = 9Z
52 = 9Z - Z
52 = 8Z
Z = 52 ÷ 8
Z = 6.5
So, average of the expenditure is $6.5
Answer: $6.5
Answer to Q125
The average age of a couple married four years ago was 25 years then. The average age of the family consisting of husband, wife and a child now is 20 years. What is the child’s present age?
Let the age of father 4 years ago be X
Let the age of mother 4 years ago be Y
The average age of a couple married four years ago was 25 years then.
So, (x + Y) ÷ 2 = 25
X + Y = 25 * 2
X + Y = 50 (eqn 1)
The average age of the family consisting of husband, wife and a child now is 20 years
Age of father after 4 years is then X + 4
Age of mother after 4 years is then Y + 4
Let age of child now be Z
So, ((X + 4) + (Y+4) + Z) ÷ 3 = 20
X + 4 + Y + 4 + Z = 20 * 3
X + Y + Z + 8 = 60
X + Y + Z = 60 - 8
X + Y + Z = 52 (eqn 2)
putting (eqn 1) into (eqn 2)
50 + Z = 52
Z = 52 - 50
Z = 2
Answer: 2 years
The average age of a couple married four years ago was 25 years then. The average age of the family consisting of husband, wife and a child now is 20 years. What is the child’s present age?
Let the age of father 4 years ago be X
Let the age of mother 4 years ago be Y
The average age of a couple married four years ago was 25 years then.
So, (x + Y) ÷ 2 = 25
X + Y = 25 * 2
X + Y = 50 (eqn 1)
The average age of the family consisting of husband, wife and a child now is 20 years
Age of father after 4 years is then X + 4
Age of mother after 4 years is then Y + 4
Let age of child now be Z
So, ((X + 4) + (Y+4) + Z) ÷ 3 = 20
X + 4 + Y + 4 + Z = 20 * 3
X + Y + Z + 8 = 60
X + Y + Z = 60 - 8
X + Y + Z = 52 (eqn 2)
putting (eqn 1) into (eqn 2)
50 + Z = 52
Z = 52 - 50
Z = 2
Answer: 2 years
Answer to Q126
A person sells a TV set at 35% loss. Had he sold it for $135 more, his loss would have been reduced by 15%. How much did he buy the TV?
Let the price of the TV = X
Let the amount he sold the TV = Y
A person sells a TV set at 35% loss
Y = (100% - 35%) of X
Y = (1 - 0.35) of X
Y = 0.65X (eqn 1)
Had he sold it for $135 more, his loss would have been reduced by 15%.
Y + 135 = ((100% - 35%) + 15%) of X
Y + 135 = (0.65 + 0.15) of X
Y + 135 = 0.8X (eqn 2)
How much did he buy the TV?
In short, what is X (A.K.A: find X 😂)
Put (eqn 1) into (eqn 2)
0.65X + 135 = 0.8X
135 = 0.8X - 0.65X
135 = 0.15X
X = 135 ÷ 0.15
X = 900
Answer: $900
A person sells a TV set at 35% loss. Had he sold it for $135 more, his loss would have been reduced by 15%. How much did he buy the TV?
Let the price of the TV = X
Let the amount he sold the TV = Y
A person sells a TV set at 35% loss
Y = (100% - 35%) of X
Y = (1 - 0.35) of X
Y = 0.65X (eqn 1)
Had he sold it for $135 more, his loss would have been reduced by 15%.
Y + 135 = ((100% - 35%) + 15%) of X
Y + 135 = (0.65 + 0.15) of X
Y + 135 = 0.8X (eqn 2)
How much did he buy the TV?
In short, what is X (A.K.A: find X 😂)
Put (eqn 1) into (eqn 2)
0.65X + 135 = 0.8X
135 = 0.8X - 0.65X
135 = 0.15X
X = 135 ÷ 0.15
X = 900
Answer: $900
Answer to Q127
If the sum of money is divided among ‘n’ children, each child will receive $60. If another child is added to the group and the amount is distributed again each child will receive $50. What is the sum of money to be distributed?
Let the money be = Y
If the sum of money is divided among ‘n’ children, each child will receive $60
Y ÷ n = 60
Y = 60n (eqn 1)
If another child is added to the group and the amount is distributed again each child will receive $50
Y ÷ (n+1) = 50
Y = 50 * (n+1)
Y = 50n + 50 (eqn 2)
putting (eqn 1) into (eqn 2)
60n = 50n + 50
60n - 50n = 50
10n = 50
n = 50 ÷ 10
n = 5
Remember "n" is the number of children, but the question says What is the sum of money to be distributed?. So what will are looking for is Y, not "n".
From (eqn 1)
Y = 60n
Y = 60 * 5
Y = 300
Answer: $300
If the sum of money is divided among ‘n’ children, each child will receive $60. If another child is added to the group and the amount is distributed again each child will receive $50. What is the sum of money to be distributed?
Let the money be = Y
If the sum of money is divided among ‘n’ children, each child will receive $60
Y ÷ n = 60
Y = 60n (eqn 1)
If another child is added to the group and the amount is distributed again each child will receive $50
Y ÷ (n+1) = 50
Y = 50 * (n+1)
Y = 50n + 50 (eqn 2)
putting (eqn 1) into (eqn 2)
60n = 50n + 50
60n - 50n = 50
10n = 50
n = 50 ÷ 10
n = 5
Remember "n" is the number of children, but the question says What is the sum of money to be distributed?. So what will are looking for is Y, not "n".
From (eqn 1)
Y = 60n
Y = 60 * 5
Y = 300
Answer: $300
Answer to Q128
Raul can do a piece of work in 20 days and Kate in 25 days. They work together for 5 days and then Kate leaves. In how many more days would Raul finish the work?
Raul can do a piece of work in 20 days
So, this means Raul works at the rate of = 1 ÷ 20 = 0.05 per day (equivalent of 5% per day)
and Kate in 25 days
and Kate works at the rate of = 1 ÷ 25 = 0.04 per day (equivalent of 4% per day)
They work together for 5 days and then Kate leaves
The percentage of work completed in that 5 days is (5% * 5) + (4% * 5) = 45% (or 0.45)
Remaining work = 100% - 45% = 55%
So, Raul does 5% of work per day and has 55% of work to complete, that will take him: 55% ÷ 5% = 11 days to complete
Answer: 11 days
Raul can do a piece of work in 20 days and Kate in 25 days. They work together for 5 days and then Kate leaves. In how many more days would Raul finish the work?
Raul can do a piece of work in 20 days
So, this means Raul works at the rate of = 1 ÷ 20 = 0.05 per day (equivalent of 5% per day)
and Kate in 25 days
and Kate works at the rate of = 1 ÷ 25 = 0.04 per day (equivalent of 4% per day)
They work together for 5 days and then Kate leaves
The percentage of work completed in that 5 days is (5% * 5) + (4% * 5) = 45% (or 0.45)
Remaining work = 100% - 45% = 55%
So, Raul does 5% of work per day and has 55% of work to complete, that will take him: 55% ÷ 5% = 11 days to complete
Answer: 11 days
Answer to Q129
A fort has a provision for 900 men for 40 days. After 20 days, 300 men join them. For how many days more will the provision last for?
A fort has a provision for 900 men for 40 days
Let the total provision be Y
Y = 900 men * 40 days = 36,000 provisions
After 20 days,
Let consumed provision be Z
Z = 900 men * 20 days = 18,000 provisions
So, remaining provision = 36,000 - 18,000 = 18,000 provisions
300 men join them
Total number of men increased to 900 + 300 = 1,200
For how many days more will the provision last for?
In other words how many days will it take 1,200 men to finish 18,000 provisions
= 18,000 ÷ 1,200
= 15
Answer: 15 days
A fort has a provision for 900 men for 40 days. After 20 days, 300 men join them. For how many days more will the provision last for?
A fort has a provision for 900 men for 40 days
Let the total provision be Y
Y = 900 men * 40 days = 36,000 provisions
After 20 days,
Let consumed provision be Z
Z = 900 men * 20 days = 18,000 provisions
So, remaining provision = 36,000 - 18,000 = 18,000 provisions
300 men join them
Total number of men increased to 900 + 300 = 1,200
For how many days more will the provision last for?
In other words how many days will it take 1,200 men to finish 18,000 provisions
= 18,000 ÷ 1,200
= 15
Answer: 15 days
Answer to Q130
If A gets 25% more than B and B gets 20% more than C, how much does C get out of $740?
If A gets 25% more than B
A = 125% of B
A = 1.25B (eqn 1)
B gets 20% more than C
B = 120% of C
B = 1.2C (eqn 2)
how much does C get out of $740?
So, A + B + C = 740 (eqn 3)
From eqn 1 and eqn 2,
A = 1.25 (1.2C)
A = 1.5C (eqn 4)
From eqn 3,
1.5C + 1.2C + C = 740
3.7C = 720
C = 720 ÷ 3.7
C = 200
Answer: $200
If A gets 25% more than B and B gets 20% more than C, how much does C get out of $740?
If A gets 25% more than B
A = 125% of B
A = 1.25B (eqn 1)
B gets 20% more than C
B = 120% of C
B = 1.2C (eqn 2)
how much does C get out of $740?
So, A + B + C = 740 (eqn 3)
From eqn 1 and eqn 2,
A = 1.25 (1.2C)
A = 1.5C (eqn 4)
From eqn 3,
1.5C + 1.2C + C = 740
3.7C = 720
C = 720 ÷ 3.7
C = 200
Answer: $200
Answer to Q131
You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question each. Except, one lies and one tells the truth, and you don't know which is which.
So, what would you ask?
There are several ways to get the correct answer from the twins. One of the simplest way:
1. Ask both twins "If I ask your brother for the right path, where will he point to?"
2. Both twins will point to the same path, because the lying twin will want to lie to you and he knows his brother would point to the right path so he point to the wrong path and the truth-telling twins knows his brother will lie so he points to the wrong path too.
3. The path they both point to is the wrong path, take the other path.
You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question each. Except, one lies and one tells the truth, and you don't know which is which.
So, what would you ask?
There are several ways to get the correct answer from the twins. One of the simplest way:
1. Ask both twins "If I ask your brother for the right path, where will he point to?"
2. Both twins will point to the same path, because the lying twin will want to lie to you and he knows his brother would point to the right path so he point to the wrong path and the truth-telling twins knows his brother will lie so he points to the wrong path too.
3. The path they both point to is the wrong path, take the other path.
Answer to Q132
Apple and Orange cost $250. The apple is $200 more than the orange. How much is the orange?
I could see a lot of people fell for the $50 for the orange but read the question again, it didn't say the cost of Apple is $200. If the cost of Apple is $200 then obviously that of orange will be 250 - 200 = $50, but like I said cost of Apple is not $200. The question said Apple is $200 more than Orange.
In fact, that is another way to prove $50 is not the correct answer, if Orange is $50 which makes Apple $200, then Apple is (200 - 50 = $150) more that Orange but the question said it should be $200.
Ok, enough of that, let's solve the question.
Apple and Orange cost $250
Let Apple = A
Let Orange = O
A + O = $250 (eqn 1)
The apple is $200 more than the orange
A = O + 200 (eqn 2)
How much is the orange? (AKA, find O)
putting eqn 1 and eqn 2 together
"O" + 200 + "O" = 250
2"O" = 250 - 200 (did 2"O" so you don't mistake that for twenty)
2"O" = 50
O = 50 ÷ 2
O = 25
So, Orange is $25 and that makes Apple $225
To check our answer, $225 - $25 = $200 (The apple is $200 more than the orange).
Answer: 25
Apple and Orange cost $250. The apple is $200 more than the orange. How much is the orange?
I could see a lot of people fell for the $50 for the orange but read the question again, it didn't say the cost of Apple is $200. If the cost of Apple is $200 then obviously that of orange will be 250 - 200 = $50, but like I said cost of Apple is not $200. The question said Apple is $200 more than Orange.
In fact, that is another way to prove $50 is not the correct answer, if Orange is $50 which makes Apple $200, then Apple is (200 - 50 = $150) more that Orange but the question said it should be $200.
Ok, enough of that, let's solve the question.
Apple and Orange cost $250
Let Apple = A
Let Orange = O
A + O = $250 (eqn 1)
The apple is $200 more than the orange
A = O + 200 (eqn 2)
How much is the orange? (AKA, find O)
putting eqn 1 and eqn 2 together
"O" + 200 + "O" = 250
2"O" = 250 - 200 (did 2"O" so you don't mistake that for twenty)
2"O" = 50
O = 50 ÷ 2
O = 25
So, Orange is $25 and that makes Apple $225
To check our answer, $225 - $25 = $200 (The apple is $200 more than the orange).
Answer: 25
Answer to Q135
Three types of drinks each worth $6.00/ltr, $7.50/ltr and $x/ltr are mixed in proportion of 1 : 2 : 3 to form a cocktail worth $8.50/ltr. What is the value of x in $/ltr?
Three types of drinks each worth $6.00/ltr, $7.50/ltr and $x/ltr
A = $6.00/ltr
B = $7.50/ltr
C = $x/ltr
are mixed in proportion of 1 : 2 : 3 to form a cocktail worth $8.50/ltr
1+2+3 = 6
so,
[(1÷6)*A] + [(2÷6)*B] + [(3÷6)*C] = $8.50/ltr
[(1÷6)*6] + [(2÷6)*7.5] + [(3÷6)*C] = 8.50
1 + 2.5 + 0.5C = 8.50
3.5 + 0.5C = 8.50
0.5C = 8.50 - 3.50
0.5C = 5
C = 5 ÷ 0.5
C = 10
Answer: 10.00
Three types of drinks each worth $6.00/ltr, $7.50/ltr and $x/ltr are mixed in proportion of 1 : 2 : 3 to form a cocktail worth $8.50/ltr. What is the value of x in $/ltr?
Three types of drinks each worth $6.00/ltr, $7.50/ltr and $x/ltr
A = $6.00/ltr
B = $7.50/ltr
C = $x/ltr
are mixed in proportion of 1 : 2 : 3 to form a cocktail worth $8.50/ltr
1+2+3 = 6
so,
[(1÷6)*A] + [(2÷6)*B] + [(3÷6)*C] = $8.50/ltr
[(1÷6)*6] + [(2÷6)*7.5] + [(3÷6)*C] = 8.50
1 + 2.5 + 0.5C = 8.50
3.5 + 0.5C = 8.50
0.5C = 8.50 - 3.50
0.5C = 5
C = 5 ÷ 0.5
C = 10
Answer: 10.00
Answer to Q136
Find a, b and x
From Pythagorean theorem,
(9+16)² = a² + b² (i)
b² = 16² + x² (ii)
a² = 9² + x² (iii)
from (i)
625 = a² + b² (iv)
put (ii) into (iv)
625 = a² + 16² + x²
625 = a² +256 + x² (v)
put (iii) into (v)
625 = 9² + x² + 256 + x²
625 = 81 + x² + 256 + x²
625 = 2x² + 337
2x² + 337 - 625 = 0
2x² - 288 = 0
2x² = 288
x² = 288 ÷ 2
x² = 144
x = √144
x = 12
put x into (v)
625 = a² +256 + x²
625 = a² + 256 + 144
625 = a² + 400
a² = 625 - 400
a² = 225
a = √225
a = 15
From (ii)
b² = 16² + x²
b² = 256 + 144
b² = 400
b = √400
b = 20
So, x = 12, a = 15, b = 20
Find a, b and x
From Pythagorean theorem,
(9+16)² = a² + b² (i)
b² = 16² + x² (ii)
a² = 9² + x² (iii)
from (i)
625 = a² + b² (iv)
put (ii) into (iv)
625 = a² + 16² + x²
625 = a² +256 + x² (v)
put (iii) into (v)
625 = 9² + x² + 256 + x²
625 = 81 + x² + 256 + x²
625 = 2x² + 337
2x² + 337 - 625 = 0
2x² - 288 = 0
2x² = 288
x² = 288 ÷ 2
x² = 144
x = √144
x = 12
put x into (v)
625 = a² +256 + x²
625 = a² + 256 + 144
625 = a² + 400
a² = 625 - 400
a² = 225
a = √225
a = 15
From (ii)
b² = 16² + x²
b² = 256 + 144
b² = 400
b = √400
b = 20
So, x = 12, a = 15, b = 20