# Past Year CBSE Board Paper

2017 Class 10 Math Set 3 Q29. Quadratic Equation

#### Video Explanation

Let A take ‘a’ days to finish the work.
Let B take ‘b’ days to finish the work.
A takes 6 days lesser than B to do a work i.e., a = b – 6 ........... (1)

Together, they finish the work in 4 days. So, in one day they will complete $$frac{1}{4}$ of the work. In one day, A will complete $\frac{1}{a}$ of the work. In one day, B will complete $\frac{1}{b}$ of the work. Together they will complete$ ${$frac {1} {a}+\frac {1} {b}}$) of the work in one day. Therefore, $\frac{1}{a}$ + $\frac{1}{b}$ = $\frac{1}{4}$ ...........$2)

Substitute (a = b – 6) in equation (2)
So, $$frac{1}{b - 6}$+ $\frac{1}{b}$ = $\frac{1}{4}$ $\frac{b + b - 6}{$b - 6$b}) = $$frac{1}{4}$ Cross multiplying the denominators we get 4$2b – 6) = (b – 6)b
8b – 24 = b2 – 6b
b2 – 14b + 24 = 0

Factorize b2 – 14b + 24 = 0
b2 – 12b – 2b + 24 = 0
(b – 12)(b – 2) = 0
Or b = 12 or b = 2

If b = 2, a = b – 6 = 2 – 6 = -4
Number of days cannot be negative. So, b cannot be 2.
The only value that b takes is 12. i.e., B takes 12 days to finish the work.

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