Question

A and B can complete work together in 5 Days. If A works at twice his speed and B at half
of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete the Job.
a. 10
b. 12
c. 15
d. 18

Answer 1

Here's your answer!!

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Let the work done by A in one day be 1/a

And work done by B in one day be 1/b

It's given that,

(A+B) can complete the work in 5 days.

(A+B)'s one day work =

$= > \frac{1}{a} + \frac{1}{b} = \frac{1}{5}$


$= > \frac{(a + b)}{ab} = \frac{1}{5} \\ = > ab = 5(a + b)........(1)$


Now,

If A work twice his speed and B work at half of his speed work will be complete in 4 days.

So,

Twice speed of A =

$= > \frac{2}{a} ( \: for \: ex = \frac{2}{14} = 7)$

Half speed of B =


$= > \frac{1}{2 b} ( \: for \: ex \: \frac{1}{2 \times 14 } = \frac{1}{28} )$


A/q

$= > \frac{2}{a} + \frac{1}{2b} = \frac{1}{4}$

$= > \frac{4a + b}{2ab} = \frac{1}{4}$


$= > 2ab = 4(4a + b) \\ = > 2ab = 16a + 4b \\ = > 2ab = 2(8a + 2b) \\ = > ab = 8a + 2b......(2)$

By putting value of ab in equation (1) ,we get ,

$= > ab = 5(a + b)$

$= > 8a + 2b = 5a + 5b$

$= > 8a - 5a = 5b - 2b$

$= > 3a = 3b$

$3 \: get \: cancelled \: from \: both \: side$
Hence,

$= > a = b$

It means number of day work done alone by A is equal to the number of days work done by B alone.

Therefore,

We can say that,

$= > \frac{1}{a} + \frac{1}{a} = \frac{1}{5}$

$= > \frac{1 + 1}{a} = \frac{1}{5}$

$= > \frac{2}{a} = \frac{1}{5}$

$= > a = 10$

Hence,

A can alone complete the work in 10 days.

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Hope it helps you!! :)