If 11 men and 16 women can do a piece of work in 6 days and 7 men and 9 women can do it in 10 days,

M4maths Previous Puzzles

12 Jul 2018 Work & Time

If 11 men and 16 women can do a piece of work in 6 days and 7 men and 9 women can do it in 10 days,

how many days will 15 women and 5 men take to do it?

OPtion

1) 7.75
2) 8.00
3) 8.25
4) 8.50
5) 8.70
6) 9.00
7) 9.25
8) 8.66
9) 9.75
10) None of these

Solution

Let a man's daily work is x units and that of a woman is y units.
So total amount of work, W = 6(11x + 16y) = 10(7x + 9y)

Solving we get, 66x - 70x = 90y - 96y
=> 4x = 6y
=> 2x = 3y


Now, 11 x + 16 y can do work in 6 days.
So, 33y/2 + 16 y can do work in 6 days.
So, 65y/2 can do work in 6 days.

Now, 5x + 15y = 15y/2 + 15y = 45y/2

Hence, if 65y/2 can do work in 6 days, 45y/2 can do work in ((65y/2)*6)/45y/2 = 8.66 days.

Option 8)

Correct Option: 8 Best Solution (1)

SAYAN CHATTERJEE   6 years AGO

11/x+ 16/y= 1/6
7/x+ 9/y = 1/10.
On solving, x= 130 & y= 195.
So, time taken = 1/(5/130+15/195)= 8.66.
Option 8.

Like? Yes (3) | No