A museum has an average of 640 visitors on each Saturdays and Sundays, while 310 visitors on other days. The average number of visitors per day in a month of 30 days beginning with a Saturday is-
Anonymous Quiz
6%
(a) 560
26%
(b) 240
14%
(c) 620
53%
(d) 420
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👆Ans. D
Explanation:
➡️ In a month of 30 days beginning with Saturday, we will have 5 Saturdays, 5 Sundays and 20 Other days.
➡️ Visitors on 5 Saturdays = 640 × 5 = 3200
➡️ Visitors on 5 Sundays = 640 × 5 = 3200
➡️ Visitors on Other days = 310 × 20 = 6200
➡️ So, Total number of visitors in 30 days = 3200 + 3200 + 6200 = 12600
➡️ Average number of visitors per day = 12600/30 = 420
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Explanation:
➡️ In a month of 30 days beginning with Saturday, we will have 5 Saturdays, 5 Sundays and 20 Other days.
➡️ Visitors on 5 Saturdays = 640 × 5 = 3200
➡️ Visitors on 5 Sundays = 640 × 5 = 3200
➡️ Visitors on Other days = 310 × 20 = 6200
➡️ So, Total number of visitors in 30 days = 3200 + 3200 + 6200 = 12600
➡️ Average number of visitors per day = 12600/30 = 420
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Rohan works in a sanitizer factory. In a 176 ltr mixture of glycer and alcohol, there’s 80% alcohol. How much alcohol should be evaporated from the mixture to reduce its percentage to 60%?
Anonymous Quiz
10%
(a) 78 ltr
63%
(b) 88 ltr
23%
(c) 72 ltr
4%
(d) 76 ltr
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👆Ans. B
Explanation:
➡️ Ratio of glycer and alcohol in the mixture = 20 : 80 = 1 : 4
➡️ So, Quantity of glycer in the solution = 176 × 1/(1 + 4) = 35.2 ltr
➡️ So, quantity of alcohol in the solution = 176 – 35.2 = 140.8 ltr
➡️ In the final mixture, alcohol is 60% and glycol is 40%.
➡️ 40% corresponds to 35.2 litres.
➡️ 60% corresponds to 35.2 × (60%/40%) = 52.8 litres.
➡️ So, Quantity of alcohol that should be evaporated = 140.8 litr – 52.8 ltr = 88 ltr
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Explanation:
➡️ Ratio of glycer and alcohol in the mixture = 20 : 80 = 1 : 4
➡️ So, Quantity of glycer in the solution = 176 × 1/(1 + 4) = 35.2 ltr
➡️ So, quantity of alcohol in the solution = 176 – 35.2 = 140.8 ltr
➡️ In the final mixture, alcohol is 60% and glycol is 40%.
➡️ 40% corresponds to 35.2 litres.
➡️ 60% corresponds to 35.2 × (60%/40%) = 52.8 litres.
➡️ So, Quantity of alcohol that should be evaporated = 140.8 litr – 52.8 ltr = 88 ltr
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In a horse race, for the first round Kalicharan makes his horse run at an average speed of 40 km/h, and in the second round he increases the speed by 50%. What is the average speed of the horse in the whole race?
Anonymous Quiz
7%
(a) 38 km/h
19%
(b) 52 km/h
67%
(c) 48 km/h
8%
(d) 64 km/ hr
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👆Ans. C
Explanation:
➡️ When a person travels a distance at a speed of x km/h and again the same distance at a speed of y km/h, then the average speed of the journey is given by (2xy)/(x + y).
➡️ Speed of horse in first round = 40 km/h
➡️ Speed of horse in second round = (40 x 150)/100 = 60 km/hr
➡️ And the distance travelled is same.
➡️ So, average speed = (2 × 40 × 60)/(40 + 60) = 2 × 4 × 6 = 48 km/hr
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Explanation:
➡️ When a person travels a distance at a speed of x km/h and again the same distance at a speed of y km/h, then the average speed of the journey is given by (2xy)/(x + y).
➡️ Speed of horse in first round = 40 km/h
➡️ Speed of horse in second round = (40 x 150)/100 = 60 km/hr
➡️ And the distance travelled is same.
➡️ So, average speed = (2 × 40 × 60)/(40 + 60) = 2 × 4 × 6 = 48 km/hr
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Ram and Sunita have some money. Product of the amounts of their money is Rs. 308700, and it’s known that Sunita has less money than Ram. If HCF of their money is Rs. 105, then how much money does Ram has?
Anonymous Quiz
15%
(a) Rs. 420
63%
(b) Rs. 735
17%
(c) Rs. 815
4%
(d) Rs. 675
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👆Ans. B
Explanation:
➡️ Let Ram and Sunita have Rs. 105x and Rs. 105y amounts respectively.
➡️ ∴ 105x × 105y = 308700
➡️ Or 105x × 105y = (105 × 7) × (105 × 4)
➡️ We know that, Sunita has less money than Ram. So, x > y.
➡️ ∴ x = 7 and y = 4
➡️ Hence, Ram has 105x = 105 × 7 = Rs. 735.
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Explanation:
➡️ Let Ram and Sunita have Rs. 105x and Rs. 105y amounts respectively.
➡️ ∴ 105x × 105y = 308700
➡️ Or 105x × 105y = (105 × 7) × (105 × 4)
➡️ We know that, Sunita has less money than Ram. So, x > y.
➡️ ∴ x = 7 and y = 4
➡️ Hence, Ram has 105x = 105 × 7 = Rs. 735.
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A tank is half filled. It is attached with two pumps P and Q, which can fill an empty tank in 16 minutes and 20 minutes respectively. If both the pumps are opened simultaneously, then how much time would it take to fill the tank?
Anonymous Quiz
15%
(a) 80/9 min
20%
(b) 70/9 min
61%
(c) 40/9 min
4%
(d) 76/9 min
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👆Ans. C
Explanation:
➡️ Capacity of the tank = L.C.M. of 16 and 20 = 80 units
➡️ Capacity of half-filled tank = 80/2 = 40 units
➡️ Efficiency of first pump = 80/16 = 5
➡️ Efficiency of second pump = 80/20 = 4
➡️ Time taken to fill the half-filled tank = 40/(5 + 4) = 40/9 min
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Explanation:
➡️ Capacity of the tank = L.C.M. of 16 and 20 = 80 units
➡️ Capacity of half-filled tank = 80/2 = 40 units
➡️ Efficiency of first pump = 80/16 = 5
➡️ Efficiency of second pump = 80/20 = 4
➡️ Time taken to fill the half-filled tank = 40/(5 + 4) = 40/9 min
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18 tractors can finish a work in 12 days and 12 backhoe loaders can finish the same work in 9 days. What is the work efficiency ratio of a tractor and a backhoe loader?
Anonymous Quiz
19%
(a) 2 : 1
19%
(b) 3 : 4
48%
(c) 1 : 2
14%
(d) 4 : 3
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👆Ans. C
Explanation:
➡️ 18 tractors can finish a work in 12 days.
➡️ So, 1 tractor can finish the same work in 18×12 days.
➡️ So, efficiency of a tractor = 1/(18×12)
➡️ 12 backhoe loaders can finish the same work in 9 days.
➡️ So, 1 backhoe loader can finish the same work in 12×9 days.
➡️ So, efficiency of a backhoe loader = 1/(12×9)
➡️ Required ratio = 1/(18×12):1/(12×9) = (12×9):(18×12) = 1 : 2
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Explanation:
➡️ 18 tractors can finish a work in 12 days.
➡️ So, 1 tractor can finish the same work in 18×12 days.
➡️ So, efficiency of a tractor = 1/(18×12)
➡️ 12 backhoe loaders can finish the same work in 9 days.
➡️ So, 1 backhoe loader can finish the same work in 12×9 days.
➡️ So, efficiency of a backhoe loader = 1/(12×9)
➡️ Required ratio = 1/(18×12):1/(12×9) = (12×9):(18×12) = 1 : 2
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Dhanraj decided to divide his total savings among his three kids A, B and C in the ratio of 3:7:5. If the difference between A’s and B’s share is Rs. 760, then what must be the share of C?
Anonymous Quiz
3%
(a) Rs. 870
20%
(b) Rs. 700
75%
(c) Rs. 950
2%
(d) Rs. 790
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👆Ans. C
Explanation:
➡️ Ratio of A, B and C’s part = 3:7:5
➡️ Let their shares be 3x, 7x and 5x.
➡️ Difference between A’s and B’s part = 760
➡️ So, 7x – 3x = 760
➡️ Or 4x = 760
➡️ Or x = 760/4 = 190
➡️ So, C’s part = 5x = 5 × 190 = Rs. 950
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Explanation:
➡️ Ratio of A, B and C’s part = 3:7:5
➡️ Let their shares be 3x, 7x and 5x.
➡️ Difference between A’s and B’s part = 760
➡️ So, 7x – 3x = 760
➡️ Or 4x = 760
➡️ Or x = 760/4 = 190
➡️ So, C’s part = 5x = 5 × 190 = Rs. 950
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13 students are standing in a row. The mean age of first seven students is 18, and the mean age of last seven students is 20. If the mean age of all the students is 19, then what must be the age of the seventh student in the row?
Anonymous Quiz
7%
(a) 17
14%
(b) 18
73%
(c) 19
7%
(d) 20
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👆Ans. C
Explanation:
➡️ Mean age of the first seven students = 18
➡️ Then, sum of first seven students’ ages = 7 × 18 = 126
➡️ Mean age of last seven students = 20
➡️ Then, sum of last seven students’ ages = 7 × 20 = 140
➡️ Mean age of all 13 students = 19
➡️ Then, sum of all 13 students’ ages = 13 × 19 = 247
➡️ So, seventh student’s age = (126 + 140) – 247 = 19
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Explanation:
➡️ Mean age of the first seven students = 18
➡️ Then, sum of first seven students’ ages = 7 × 18 = 126
➡️ Mean age of last seven students = 20
➡️ Then, sum of last seven students’ ages = 7 × 20 = 140
➡️ Mean age of all 13 students = 19
➡️ Then, sum of all 13 students’ ages = 13 × 19 = 247
➡️ So, seventh student’s age = (126 + 140) – 247 = 19
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What number should come in place of the question mark (?) in the following series.
17, 23, 35, ?, 107, 203
17, 23, 35, ?, 107, 203
Anonymous Quiz
22%
(a) 53
16%
(b) 55
55%
(c) 59
7%
(d) 90
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👆Ans. C
Explanation:
➡️ 17 + 6 = 23
➡️ 23 + 6×2 = 23 + 12 = 35
➡️ ? = 35 + 12×2 = 35 + 24 = 59
➡️ 59 + 24×2 = 59 + 48 = 107
➡️ 107 + 48×2 = 107 + 96 = 203
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Explanation:
➡️ 17 + 6 = 23
➡️ 23 + 6×2 = 23 + 12 = 35
➡️ ? = 35 + 12×2 = 35 + 24 = 59
➡️ 59 + 24×2 = 59 + 48 = 107
➡️ 107 + 48×2 = 107 + 96 = 203
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In the series 905, 812, 911, 678, 351, 796, if all digits of the numbers are arranged in ascending order within the number, then which of the following would become the fourth smallest number?
Anonymous Quiz
8%
(a) 911
49%
(b) 351
31%
(c) 812
12%
(d) None of the above
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👆Ans. B
Explanation:
➡️ Given series: 905, 812, 911, 678, 351, 796
➡️ If all digits of the numbers are arranged in ascending order within the number, then we get: 059, 128, 119, 678, 135, 679
➡️ Arranging the above series in descending order, we get: 679, 678, 135, 128, 119, 059
➡️ Fourth smallest number is 135, i.e. number 351.
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Explanation:
➡️ Given series: 905, 812, 911, 678, 351, 796
➡️ If all digits of the numbers are arranged in ascending order within the number, then we get: 059, 128, 119, 678, 135, 679
➡️ Arranging the above series in descending order, we get: 679, 678, 135, 128, 119, 059
➡️ Fourth smallest number is 135, i.e. number 351.
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WR-CSM-2023-081223-ENG (1).pdf
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