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# A Takes 10 Days Less than the Time Taken by B to Finish a Piece of Work. If Both a and B Together Can Finish the Work in 12 Days, Find the Time Taken by B to Finish the Work. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

#### Solution

Let B alone takes days to finish the work. Then, B’s one day’s work = 1/x.

Similarly, alone can finish it in (x - 10) days to finish the work. Then, A’s one day’s work =1/(x-10).

It is given that

A’s one day’s work + B’s one day’s work = (A + B)’s one day’s work

1/x+1/(x-10)=1/12

(x-10+x)/(x(x-10))=1/12

(2x-10)/(x^2-10x)=1/12

x2 - 10x = 12(2x - 10)

x2 - 10x = 24x - 120

x2 - 10x - 24x + 120 = 0

x2 - 34x + 120 = 0

x2 - 30x - 4x + 120 = 0

x(x - 30) - 4(x - 30) = 0

(x - 30)(x - 4) = 0

x - 30 = 0

x = 30

Or

x - 4 = 0

x = 4

But x = 4 is not correct.

therefore, x = 30 is correct

Hence, the time taken by to finish the work in x = 30 days

Is there an error in this question or solution?

#### APPEARS IN

Solution A Takes 10 Days Less than the Time Taken by B to Finish a Piece of Work. If Both a and B Together Can Finish the Work in 12 Days, Find the Time Taken by B to Finish the Work. Concept: Solutions of Quadratic Equations by Factorization.
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