Solving a Quadratic Equation by Factorization Method
A and B can d...
Question
A and B can do a piece of work in x and x+16 days respectively. If both working together can do it in 15 days, the value of x will be.
A
24
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B
22
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C
20
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Solution
The correct option is A 24 Given: A can do a piece of work in x days and B in x+16 days.
Work done by A in one day = 1x
Work done by B in one day = 1x+16
Work done by A and B together in one day = 115 ⇒1x + 1x+16 = 115 ⇒2x+16x(x+16)=115 ⇒x2+16x=15(2x+16) ⇒x2−14x−240=0 ⇒x2−24x+10x−240=0 ⇒x(x−24)+10(x−24)=0 ⇒(x−24)(x+10)=0 ⇒x=24orx=−10 ⇒x=24 as x cannot be negative.