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Three men A. B and C working , together ...

Three men A. B and C working , together can do a job in 6 hours less time than A alone, in 1 hour less time than B alone and in one half the time needed by C when working alone. Then A and B together can do the job in

A

`2/3`घंटा

B

`3/4` घंटा

C

`3/2` घंटा

D

`4/3`घंटा

Text Solution

Verified by Experts

The correct Answer is:
B
माना कि A, B तथा C तीनों मिलकर कार्य x घंटे में पूरा करते हैं।
`therefore` A द्वारा लिया गया समय `=x+6`
B द्वारा लिया गया समय = `x + 1 `
तथा C द्वारा लिया गया समय `= 2x`
`therefore 1/(x + 6) + 1/(x +1) + 1/(2x) = 1/x`
`implies 1/(x + 6) + 1/(x + 1) = 1/x - 1/(2x)`
`(2x + 7)/(x^2 + 7x + 6) = 1/(2x)`
`implies 3x^2 + 7x - 6 = 0`
`implies x = 2/3`
A की कार्य क्षमता = `1/(2/3 + 6) = 3/20`
B की कार्य क्षमता =`1/(2/3 + 1) = 3/5`
A तथा B की कार्य क्षमता `= 3/20 + 3/5 = 15/20 = 3/4`
अतः दोनों मिलकर कार्य `3/4` के घंटे में पूरा करेंगे।
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