Time and Work MCQ | Page 10 of 10 | with Solutions for Competitive exams

time and work questions answer

Answer the time and work questions and check your answers

A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman alone take to complete the work?

(a) 9 days

(b) 21 days

(d) 27 days

(e) 30 days

Answer for the practice question on Time and Work is (a)

Work done by 1 woman in 1 day = \(\displaystyle \frac{1}{3}-\frac{1}{6}-\frac{1}{{18}}=\frac{{6-3-1}}{{18}}=\frac{1}{9}\)

Therefore, Woman will do the work in 9 days.

Alternate Method :

Here, x = 3, y = 6 and z = 18

Therefore, Required time = \(\displaystyle \frac{{xyz}}{{yz-x(y+z)}}days\)

\(\displaystyle \frac{{3\times 6\times 18}}{{6\times 18-3(6+18)}}=\frac{{324}}{{108-3\times 24}}=\frac{{324}}{{36}}=9\)

If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?

(a) 260

(b) 240

(d) 520

(e) 420

Time and Work questions answer is (a)

10 men = 20 boys

1 man = 2 boys

8 men + 4 boys

= (16 + 4) boys = 20 boys

Hence, 8 men and 4 boys will make 260 mats in 20 days.

One man and one woman together can complete a piece of work in 8 days. A man alone can complete the work in 10 days. In how many days can one woman alone complete the work ?

(a) \(\displaystyle \frac{{140}}{9}\) days

(b) 30 days

(d) 42 days

(e) 45 days

Time and Work questions answer is (c)

Work done by 1 woman in 1 day

\(\displaystyle \frac{1}{8}-\frac{1}{{10}}=\frac{{5-4}}{{40}}=\frac{1}{{40}}\)

Therefore, One woman will complete the work in 40 days.

Alternate Method :

Here, x = 10 and y = 8

Woman can do work in = \(\displaystyle (\frac{{xy}}{{x-y}})days=(\frac{{10\times 8}}{{10-8}})=40days\)

6 men and 8 women can do a work in 10 days, Then 3 men and 4 women can do the same work in

(a) 24 days

(b) 20 days

(d) 18 days

(e) 28 days

Time and Work questions answer is (b)

6m + 8w = 10 days

\(\displaystyle \Rightarrow \) 2 (3m + 4w) = 10 days

\(\displaystyle \Rightarrow \) 3m + 4w = 20 days

[Since the workforce has become half of the original force, so number of days must be double].

Alternate Method :

Let us assume efficiency of 6 men = efficiency of 8 men.

A = 6, a = 20

B = 8, b = 20

\(\displaystyle {{A}_{1}}=3,{{B}_{1}}=4\)

Therefore, Required time = \(\displaystyle \frac{1}{{\frac{{{{A}_{1}}}}{{A\times a}}+\frac{{{{B}_{1}}}}{{B\times b}}}}\)

= \(\displaystyle \frac{1}{{\frac{3}{{6\times 20}}+\frac{4}{{8\times 20}}}}\)

= \(\displaystyle \frac{1}{{\frac{1}{{40}}+\frac{1}{{40}}}}=\frac{{40}}{2}=20days\)

2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work ?

(a) 8 \(\displaystyle \frac{1}{2}\) days

(b) 7 days

(d) 2 days

(e) 6 \(\displaystyle \frac{1}{2}\) days

Time and Work questions answer is (c)

According to the question,

20 men + 30 boys = 24 men + 16 boys

Therefore, 4 men = 14 boys

\(\displaystyle \Rightarrow \) 2 men = 7 boys

\(\displaystyle \Rightarrow \) 2 men + 1 boy = 8 boys

\(\displaystyle \Rightarrow \) 2 men + 3 boys = 10 boys

By \(\displaystyle {{M}_{1}}{{D}_{1}}={{M}_{2}}{{D}_{2}}\)

\(\displaystyle 10\times 10=8\times {{D}_{2}}\)

\(\displaystyle {{D}_{2}}=\frac{{10\times 10}}{8}=\frac{{25}}{2}=12\frac{1}{2}days\)

3 men and 4 boys can complete a piece of work in 12 days. 4 men and 3 boys can do the same work in 10 days. Then 2 men and 3 boys can finish the work in number of days is

(a) \(\displaystyle 17\frac{1}{2}\) days

(b) \(\displaystyle 5\frac{5}{{11}}\) days

(d) 22 days

(e) 25 days

Time and Work questions answer is (a)

12 (3 men + 4 boys) = 10 (4 men + 3 boys)

\(\displaystyle \Rightarrow \) 36 men + 48 boys = 40 men + 30 boys

\(\displaystyle \Rightarrow \) 4 men = 18 boys or 2 men = 9 boys

Therefore, 4 men + 3 boys = 21 boys who do the work in 10 days and, 2 men + 3 boys = 12 boys

\(\displaystyle {{M}_{1}}{{D}_{1}}={{M}_{2}}{{D}_{2}}\)

\(\displaystyle 21\times 10=12\times {{D}_{2}}\)

\(\displaystyle {{D}_{2}}=\frac{{21\times 10}}{{12}}=\frac{{35}}{2}=17\frac{1}{2}days\)

Hope the content of this page MCQ on Time and Work is useful for your preparation. Rankers Hub is your one-stop solution for Time and Work Multiple Choice Questions (MCQ), especially for aspirants preparing for Banking, SSC, Railways, and Defence exams. Time and Work problems are a critical component of the quantitative aptitude sections, objective questions are asked in exams like IBPS PO, IBPS Clerk, IBPS RRB, SBI PO, SBI Clerk, RBI Grade B, RBI Assistant, SSC CGL, SSC CHSL, SSC GD, RRB NTPC, RRB Group D, CAPF, NDA, CDS, AFCAT, and more. Our comprehensive collection of objective questions on Time and Work are designed to enhance your understanding and problem-solving skills. With a variety of practice questions covering previous years questions and also MCQ ranging from basic to advanced levels, along with detailed explanations, this platform equips you to excel in speed, accuracy, and confidence. Start practicing today and ensure your success in these competitive exams with Rankers Hub.

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