Choose the correct answer from the alternatives given.
15 men can complete a work in 10 days while 20 boys can complete the same work in 15 days. How many days will 10 men and 10 boys take to complete the remaining work?
(a). 10
(b). 8
(c).12
(d). 9

Hint:– Break down each phrase of the question to understand it better. Then find out the rate at which the work is completed with respect to boys, men. Also, find out the amount of work that can be done in one day by men and boys. Change it into one parameter to get the answer.

Complete step-by-step solution -
Given Data – 15 men can do the work in 10 days
∴One day work is completed by 15 × 10 men = 150 men.
Also, 20 boys can complete the work in 15 days
∴In one day the work is completed by 20 × 15 = 300 boys.
∴Work of 150 men = Work of 300 boys
⟹Work of one man = = Work of 2 boys
⟹Work of 10 men = 2 × 10 = Work of 20 boys
We should find out work done by 10 men and 10 boys = 10(2) + 10 = 30 boys
Also given, 20 boys do the work in 15 days
⟹30 boys can do it in =10 days.
Hence, Option A is the correct answer.

Note:–The key to solving this type of question is to understand exactly what was given and make relations accordingly. Then we find out the rate at which the work can be done with respect to each parameter. Then build a relation for the two parameters and convert everything into a single parameter to determine the answer.