यदि 40 पुरुष या 60 महिलाएँ या 80 बच्चे किसी काम को 6 महीने में समाप्त कर सकते है तो 10 पुरुष ,10 महिलाएँ तथा 10 बच्चे मिलकर काम को कितने दिनों में समाप्त करेंगे ?

Options

A. `5(6)/(13)` months
B. 6 months
C. `5(7)/(13)` months
D. `11(1)/(13)` months

Answer

c

Explanation

(d) 40 men = 60 women = 80children
2 men = 3 women =4 children
2 men = 3 women
1 women `=(2)/(3)` men `to` 10 women
`to (2)/(3) xx10 = (20)/(3)` men
similarly
2 men = 4 chilren `(10)/(2)`=5 men
10 men + 10 women +10 children
=10men + 10 women + 10 children
`=10 "men" +(20)/(3)+5 implies (30+20+15)/(3)`
10 men + 10women + 10 children
`=(65)/(3) men `
40 men can do a piece of work in 6 months
1 man can do a piece of work in `6xx40`
`(65)/(3)` men can do a piece of work in `(6xx40)/((65)/(3))= 11(1)/(3)` months
Alternate
40m = 60w = 18C
2 m = 3W = 4C
m:W:c= 6:4:3 (efficiency ) total time taken by (10m + 10W + 10C)
`("total work ")/("Efficiency")=(1440)/(130)=11(1)/(13)`days