Question

2 men and 5 boys can do a piece of work in 4 days while 4 men and 4 boys can do it in 3 days how long would it take one man or one boy to do it

Answer 1

let time taken by 1 men per day= 1/x
let time taken by 1 boy per day = 1/y
according to question

2/x +5/y = 1/4
and also
4/x+ 4/y = 1/3

after solving 1st equation we get

let 1/x = p and 1/y = q
there fore 2p+5q = 1/4
8p+20q= 1 ..........(1)

2nd eq.

same with it

4p+4q =1/3

12p+12q = 1..........(2)

by substitution method
in 1st eq.
p=1-20q/8....(3)
put eq 3 in eq 2

12(1-20q/8)+4q =1

it gives

(12-240q+32q)=4

-208q = -8

q = 8/208

q= 1/16

put q = 1/16 in eq 3

p=(1-20×1/16)/8

then after solving it u will get value of p

then put value of p and q in 1/x and 1/y to get x and y

this taked lot of efforts hope you will understand
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Answer 2

Answer:

Total time taken by one man to complete the job = 18 days and Total time taken by one boy to complete the job = 36 days

Step-by-step explanation:

Let one man complete the work in 1/x days and one boy completes the work in 1/y days.

Now, 2 men and 5 boys can finish a piece of job in 4 days

⇒ 2x + 5y = 1/4

⇒ 8x + 20y = 1 .........(1)

Also, 4 men and 4 boys finish it in 3 days

⇒ 4x + 4y = 1/3

⇒ 12x + 12y = 1 ........(2)

Now, solving the equations (1) and (2)

We get 1/x = 18 and 1/y = 36

So, Total time taken by one man to complete the job = 18 days and Total time taken by one boy to complete the job = 36 days