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For the same amount of work an adult takes 6 hours less than a boy .if together they complete the work in 13 hours and 20 minutes find how much time will the boy alone take to complete the work

Posted by Suman Suman 7 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Rajeev Malhotra 7 years, 7 months ago

let a boy takes x hours to complete the work. So an adult will take x-6 hours to complete the work. So work done by boy in 1 hour= 1/x and work done by adult in 1 hour = 1/x-6

They complete the work in 13 hours and 20 minutes. So they complete the work in 40/3 hours. So work done by both in 1 hour = 3/40

$1/x+1/x-6 = 3/40$

$2x-6/x(x-6) = 3/40$

By cross multiplication, we get

$80x-240= 3x^2-18x$

$3x^2-98x+240 = 0$

$3x^2-90x-8x+240 = 0$

$3x(x-30) -8(x-30) = 0$

$(x-30)(3x-8) = 0$

$x= 30 or 8/3$

So x = 30. So a boy can alone complete work in 30 hours.

1Thank You

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