Question

'अ', 'ब', 'क' हे तिघे मिळून एक काम 12 दिवसांत संपवितात. 'अ' हा 'ब' च्या दुप्पट काम करतो. तर 'क' हा 'अ'
आणि 'ब' यांच्या एकत्रित कामाच्या 1/3 काम करतो. तर एकटा 'क' ते काम स्वतंत्रपणे किती दिवसांत पूर्ण करेल ?
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Answer 1

Given:

A, B & C together does one work in 12 days

A does works twice of B

C does 1/3 work of A and B

To find:

In how many days C will complete the work alone

Solution:

Let's assume that in 1 day A will do "x" amount of work.

So, according to the question, we get

The work done by B in 1 day = $\frac{x}{2}$

and

The work done by C in 1 day = $\frac{1}{3}[A + B]$ = $\frac{1}{3}[x + \frac{x}{2} ]$ = $\frac{1}{3}[\frac{2x+ x}{2} ] = \frac{1}{3}[\frac{3x}{2} ] = \frac{x}{2}$

Now, all 3 of them does one work in 12 days, so

The work done by A, B & C together in 1 day will be = $\frac{1}{12}$

$\implies \frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{1}{12}$

$\implies x + \frac{x}{2} + \frac{x}{2} = \frac{1}{12}$

$\implies \frac{2x + x + x}{2} = \frac{1}{12}$

$\implies \frac{4x}{2} = \frac{1}{12}$

$\implies2x = \frac{1}{12}$

$\implies x = \frac{1}{2 \times 12}$

$\implies \bold{x = \frac{1}{24}}$ ← A's 1 day's work

∴ The work done by C in 1 day = $\frac{x}{2}$ = $\frac{1}{24} \times \frac{1}{2} = \bold{\frac{1}{48}}$

Thus, C alone will complete the work in → 48 days.

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