Question

(a) 10
(b) 12
(c) 14
(d) 16
(e) None of these
)
11. A takes 6 days more than B to finish a work. If they together do the same work in 10 days, in
7
many days will B alone complete the same work?
(a) 24
(b) 18
(c) 9
(d) 180
(e) None of these​

Answer 1

The answer is 17 days . The correct option is (e) None of these

GIVEN

A takes 6 days more than B to finish a work.

TO FIND

If they together do the same work in 10 days, in how many days will B alone complete the same work?

SOLUTION

We can simply solve the above problem as follows;

Let, The number of days taken by B to complete the work be x

Therefore,

B's one day work = 1/x

Number of days taken by A to complete the work = x + 6 days

A's one day work = 1/x+6

Number of days taken by both A and B to complete the work = 10 days

One day work of A and B

$\frac{1}{x} + \frac{1}{x + 6} = \frac{1}{10}$

$\frac{x + 6 + x}{x(x + 6) } = \frac{1}{10}$

$\frac{2x + 6}{ {x}^{2} + 6x } = \frac{1}{10}$

20x + 60 = x² + 6x

= x² - 14x - 60 = 0

Solving the quadratic equation-

$x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a}$

= 7 + √109 = 17.44 ≈ 17 days

Hence, The answer is 17 days

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