SI Exam: Do you have time to work on time and work problems?

By Banda Ravipal Reddy

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some previous year questions and explanations on the Time and Work topic. To improve calculations speed, the aspirants must practice questions from the previous question papers.

1. A and B undertaken to do a work for Rs 6000. A alone and B alone can do not that in 6 and 8 days respectively. With the help of C, they have finished the work in 3 days. The share of B’s is (SI PRE 2018)
A. Rs 2,400 B. Rs 2,250 C. Rs 2,000 D. Rs 1,500

Ans: B

Explanation:
A = 6 days, B = 8 days and A B C = 3 days

Total work= LCM of (6, 8, 3) = 24
Efficiency of (A, B, A B C) = 4, 3 and 8

A B C=8

Efficiency of C = 8-4-3 = 1
Ratio of efficiency of A, B, C= 4: 3: 1

Total amount = 6000

B’s share = 6000×3/8= 2250

2. A piece of work can be completed by A, B and C individually in 12, 8 and 6 hours respectively. All the three worked for two hours at which point of time C left the work. The time (in minutes) taken by the other two to complete the work is: (SI PRE 2018)

A.12 B. 24 C. 62 D. 72

Ans: D

Explanation:
A= 12 hours, B = 8 hours and C = 6 hours

Total work = LCM of (12, 8, 6) = 24
Efficiency of (A, B, C) = 2, 3 and 4

The work completed in two hours = (2 3 4) × 2= 18

Remaining work = 24-18 = 6 units

Time taken by A and B to complete 2 units of work = 6/5 hours= 72 min

3. Person A completes a work W1 in 6 hours while person B completes another work W2 in 6 hours. If W2 is only equal to two-thirds of W2 then the number of hours required for A and B together to complete both W1 and W2 is (SI PRE 2018)

A. 6 B. 7 C. 5 D. 8

Ans: A

Explanation:
Suppose W2 = 1
So, according to the question: W1= 2/3
Total work i.e., W1 W2 = 1 2/3 = 5/3
Work done by A in one hour = (2/3)/6 = 1/9
Work done by B in one hour = 1/6
Total work done by A and B together in one hour = 1/9 1/6 = 5/18
Number of hours required for A and B together = (5/3)/(5/18) = 6

4. A and B can do a piece of work independently in 12 days and 16 days respectively. They worked together for 4 days and B left the work. How many more days A worked to finish the work? (SI PRE 2018)

A. 3 B. 4 C. 5 D. 6

Ans: C

Explanation:
A and B”s one day”s work =1/16 1/12 = (3 4)/48 = 7/48
(A B) 4 day’s work= 7/48×4 = 7/12
Remaining work 1-7/( 12) = 5/12
Time taken by A to finish the remaining work = (5⁄12)/(1⁄12) = 5 days

5. Two persons A and B undertake to paint a house for Rs 54,000. A alone can paint the house in 40 days and B alone can paint the house in 45 days. A and B along with a third person C completes painting in 20 days. Then, the share of C is (in rupees) (SI MAINS 2018)

A. 6000 B. 5000 C. 4000 D. 3000

Ans: D

Explanation:
A= 40 days, B = 45 days and A B C = 20 days

LCM of (A, B, A B C) is = 360

Efficiency of (A, B, A B C) = 9, 8 and 18

A B C = 18

Efficiency of C = 18-9-8 = 1

Ratio of efficiency of A, B, C = 9: 8: 1

Total amount = 54000

C’s share = 54000×1/18 = 3000

The author is the director of (SIGMA) 

Sai Institute of General Mental Ability

Hyderabad

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