A and B together can do a piece of work in 15 days. If A’s one day work is 1½ times the one

day’s work of B, find in how many days can each do the work.

Question

A and B together can do a piece of work in 15 days If As one day work is 1 times the one days work of B find in how many days can each do the work

Accepted Answer

Let As one day work be x and Bs one day work be y Then according to the first condition given in the problem we have x 32y 2x 3y 2x 3y 0 i Also given in 15 days A and B together can do a piece of work So according to this condition we have x y 115 15 x y 1 15x 15y 1 ii Multiplying equation i by 5 we get 10x 15y 0 15x 15y 1 25x 1 x 125 On substituting the value of x in equation i we get 2125 3y 0 225 3y y 275 Therefore Man A will do the work in 1x days 1125 25 days and Man B will do the work in 1y days 1275 752 37 days 27 2 men and 5 women can do a piece of work in 4 days while one man and one woman can finish it is 12 days How long would it take for 1 man to do the work Solution Lets assume that 1 man takes x days to do work and y days for women So the amount of work done by 1 man in 1 day 1x And the amount of work done by 1 woman in 1 day 1y Now The amount of work done by 2 men in 1 day will be 2x And the amount of work done by 5 women in 1 day 5y Then according to the given conditions in the problem we have 2x 5y i 1x 1y 112 ii Multiplying equation ii by 5 we get 5x 5y 512 2x 5y 3x 512 3x 5 312 3x 212 16 x 18 Therefore 1 man can do the work in 18 days

ML Aggarwal Solutions Class 9 Mathematics Solutions for Problems on Simultaneous Linear Equations Exercise 6 in Chapter 6 - Problems on Simultaneous Linear Equations