Question

3 men and 4 boys can do a piece of work in
14 days, while 4 men and 6 boys can do it in
10 days. How long would it take for 1 boy alone
to finish the same work.
please solve it by simultaneous method.
the answers are 70 days and 140 days​

Answer 1

Answer:

Given,

Ratio of men is 3:4 and inversely proportion to number of days to complete the work

Ratio of boys is 4:6 or 2:3 and inversely proportion to number of days to complete the work

Ratio of days to complete same work is 14:10 or 7:5 and inversely proportion to both number of men and number of boys

If 3 men and 4 boys can do a work in 14 days, then 3 men and 4 boys do 114th of work in a day.

If 4 men and 6 boys can do a work in 10 days, then 4 men and 6 boys do 110th of work in a day.

Let the part of the work done by men be x and let the part of the work done by boys be y done in a day

Hence,

3x+4y=114(1)

4x+6y=110(2)

By Solving equations 1 and 2

x=170

y=1140

Hence 1 man does 170th of work and 1 boy does 1140 th of work in a single day . In other words 1 man takes 70 days to complete the work and 1 boy takes 140 days to complete the work.

If 1 man takes 70 days to complete then 2 men can do the work in 35 days, because number of men and number of days to complete the work are inversely proportional