Get your basic arithmetic concepts right

By Banda Ravipal Reddy Director, SIGMA Sai Institute of General Mental Ability 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 […]

By Banda Ravipal Reddy
Director, SIGMA
Sai Institute of General Mental Ability
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.

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1. Two persons have undertaken to do a piece of work for Rs 1,200. One alone could it in 6 days and the other in 8 days. With the assistance of a boy, they finish it in 3 days. The difference between the shares of the two persons (in rupees) is (SI 2016).

A. 150. 200 C. 25 D. 300

Ans: A

Explanation:

First person 1 day’s work = 1/6 Second person 1 day’s work = 1/8 Let boy’s 1 day’s work be 1/x According to the question, ⇒ (1/6) (1/8) (1/x) = (1/3)⇒ (1/x) = (1/3) – {(1/6) (1/8)} ⇒ (1/x) = 1/24 ∴ Ratio in shares of first person, second person and boys = (1/6): (1/8): (1/24) = (1/6) × 24: (1/28) × 24: (1/24) × 24 = 4: 3: 1 The difference between shares of the two person = {(4 – 3)/(4 3 1)} × 1200 = 150

2. Two men undertaken to do a piece of work for Rs. 5,600. First man alone can do this work in 7 days while the second man alone can do this work in 8 days. If they work together and complete this work in 3 days with the help of a boy, then the amount the two men together get is (in rupees).

A. 4,000 B. 4,500 C. 4,580 D. 4,600
Ans: B

Explanation:

First man’s 1 day’s work = 1/7 Second man’s 1 day’s work = 1/8 Boy’s 1 day’s work = (1/3) – {(1/7) (1/8)} = (1/3) – (15/56) ⇒ Boy’s 1 day’s work = (11/168) ⇒ Ratio of wages of the first man, second man and boy = (1/7): (1/8): (11/168) L.C.M of 7, 8, and 168 is 168 Ratio of wages of the first man, second man and boy = (1/7) × 168: (1/8) × 168: (11/168) × 168 ⇒ Ratio of wages of the first man, second man and boy = 24: 21: 11 ∴ Total share of the amount = 24 21 11 = 56 units ⇒ First man’s share = Rs (24/56) × 5600 = Rs 2400 ⇒ Second man’s share = Rs (21/56) × 5600 = Rs 2100 The amount shares in two men together get = 2400 2100 = 4500 ∴ the amount the two men together get is Rs 4500

3. If the wages of 6 men for 15 days be Rs. 700, then the wages of 9 men for 12 days will be (in rupees).

A. 840 B. 848 C. 1,050D. 900

Ans: A

Explanation:

Let the required wages be Rs x. More men, more wages (direct proportion) Less days, less wages (direct proportion) men 6: 9 : : 700: x Days 15:12 Therefore (6 × 15 × x) = (9 × 12 × 700) =>; x = (9 × 12 × 700)/(6 ×15) = 840 Hence, the required wages are Rs 840 . men can do a work in 12 days. After 6 days of work, 4 more men were engaged to finish the work. The number of days required to complete the remaining work is.

A. 2 B. 3 C. 4 D. 5

Ans: C

Explanation:

Assume the work is 96 units.
Then 8 men can finish these 96 units of work in 12 days. Which means per day 8 men can do 8 units of work. And one man can finish one unit in one day. As the 8 men worked for 6 days, the work finished = 48 units. Still 48 units are left and 12 men can finish it in 4 days.