# QOTD-QA-Time and Work Question

2019-07-13 | Team PendulumEdu

10 men can complete a piece of work in 6 days while 20 women can do it in 10 days. How many days will 10 women and 6 men take to complete the same work together?

A. 5

B. 8

C. 10

D. 12

Solution:

According to the question, 10 men can complete a piece of work in 12 days

Thus, 1 man can complete the same piece of work in = 12 x 10 = 120 days

So, 1 man’s 1 day work will be

$$=\frac{1}{12×10 }=\frac{1}{120 }..................(I)$$

Also, 20 women can complete the same piece of work in 10 days

Thus, 1 woman can complete the work in 20 x 10 = 200 days

And, similarly 1 woman’s 1 day work will be

$$=\frac{1}{20×10 }=\frac{1}{200 }..................(II)$$

Now, we have to find the work of 10 women and 6 men

From equation (I)

10 women’s 1 day work will be

$$= 10*\frac{1}{200} =\frac{1}{20}….....(III)$$

From equation (II)

6 men’s one day work will be
$$= 6×\frac{1} {120}=\frac{1}{20}...….(IV)$$

From equation (III) and (IV), we get

10 women’s and 6 men’s 1 day work together will be

$$= 10×\frac{1} {200}+ 6*\frac{1}{120}$$

$$=\frac{1}{10}$$

Thus, 10 women + 6 men team can complete the whole work in 10 days.

Hence, (c) is the correct answer.

Time and Work questions constitutes significant portion of the total marks in Quantitative aptitude section of various exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS CLERK, IBPS SO, etc. You can try free mock tests at PendulumEdu to clear your concepts and to learn new tricks to solve such question.