Question

4 man and 6 boys can finish a piece of work in 5 days while 3 men and 4 boys can finish it in 7 days. find the time takken by 1 man alone

Answer 1

The Answer is written below:

Let the no. of day's work by men be x

Let the no. of day's work  by boys be y

4/x +6/y= 5    -(i)

3/x+4/y= 7     -(ii)

let 1/x = a and 1/y= b

4a+6b=5 *3

3a+4b=7 * 4

so,

12a+18b=15

12a+16b=28

(-)   (-)    (-)

2b=-13

b= -13/2

4a+6b =5

4a+6(-13/2)=5

4a+(-78)/2=5

8a - 78 = 5*2

8a= 88

a= 11

a= 1/x = 11      (11 days is required by men to complete the job)

b=1/y=13/2         (6.5 day is required by boys to complete the job )

x= 11, y= 6.5