need answer with this problem solving plss?

Here the rate is the number of trenches per number of hours..so rate=(number of trenched)/(number of hours)

Suppose we take x as the number of hours we need to find.

Making a table like this is the best way to solve these kind of things:

Number of men Rate

Given : 3 2/5

To find: 5 7/x

Now cross-multiply(draw an X at the centre joining the numbers to make it easier) to get this:

3 x 7/x = 5 x 2/5

21/x = 2

x=21/2=10.5 hours

3 men dig 2 trenches in 5 hours

1 man digs 2 trenches in 15 hours ( 1 man takes longer than 3)

1 man digs 1 trench in 15/2 hours ( 1 trench takes less than 2 trenches)

5 men dig 1 trench in (1/5)X15/2=3/2 hours

5 men dig 7 trenches in 7X3/2=10½ hours

10.5 hrs

let x=no. of hrs

y=no.of workers

z=rate

zxy=2

z(3)(5)=2

z=2/15

zxy = 7

(2/15)(x)(5)=7

x=10.5 hrs

3 men dig 2 trenches in -------------------------------= 5 hrs

1-----------2--------------------------------------------------= 5x3 hrs

1------------1-------------------------------------------------= 5x3/2 hrs

5----------1--------------------------------------------------= 5x3/2*5 hrs

5 ---------------7---------------------------------------= 5x3x7/2*5

--------------------------------------------------21/2= 10.5 hrs answer