Question

16 men can do a work in 5 days 12 women can do it
in 8 days while 20 boys can finish it in 6 days. 5
men, 6 women and 10 boys started work together
but after 3 days men and women left how many more
boys are needed to finish remaining workin 3/4 of a
day
16 पुरुष किसी कार्य को दिनों में, 12 महिलाएं उसी कार्य को 8 दिनों
में, जबकि लड़के इसे 6 दिनों में कर सकते हैं। 5 पुरुष, 6 महिलाए
और 10 लड़को ने एक साथ कार्य करना शुरू किया लेकिन 3 दिनो के
बाद पुरुषों और महिलाओं ने कार्य छोड़ दिया। तो ज्ञात करे कि 3/4 दिन
में शेष कार्य पूरा करने के लिए कितने और लड़को की आवश्यकता
होगी?​

Answer 1

You will often be able to ballpark or find the exact solution by just working on the multiples of the given equations.

Say rate of work of each man is M and that of each woman is W.

Given: 12M + 16W = 1/5 (Combined rate done per day)

______3M + 4W = 1/20 (in lowest terms) ...........(I)

Given: 13M + 24W = 1/4 ......................................(II)

Reqd: 7M + 10W = ?

Using equations (I) and (II) we need to find the sum of 7M and 10W. We can get a multiple of 7M in various ways:

(3M + 4W = 1/20) * 5 gives 15M + 20W = 1/4

Adding this to equation II, we get 28M + 44W = 1/2

7M + 11W = 1/8

7 men and 11 women complete the work in 8 days. 7 men and 10 women will take a little more than 8 days to complete the work. If you do get such a question in GMAT, you will easily be able to manipulate the equations to get the desired equation. Finding the values of M and W is way too painful to interest GMAT.