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Aparna can do a work in 12 days. Together working with Pratima, Aparna and Pratima received their wages in the ratio 4 ∶ 3. In how many days can Pratima do the work alone?

Aparna can do a work in 12 days. Together working with Pratima, Aparna and Pratima received their wages in the ratio 4 ∶ 3. In how many days can Pratima do the work alone? Correct Answer 16 days

Let us assume that Pratima can do the work alone in ‘x’ days

Aparna’s 1 day work = 1/12

Pratima’s 1 day work = 1/x

Now, Ratio of their wages = Ratio of their 1 day work

⇒ 4 ∶ 3 = (1/12) ∶ (1/x)

⇒ 4/3 = x/12

⇒ x = 12 × (4/3) = 16 days

∴ Pratima can do the work alone in 16 days

Alternate Solution

We know, Time taken ∝ 1/Efficiency ∝ 1/Wage

Here, ratio of wage = 4 : 3

Hence, ratio of days = 3 : 4 = 3x : 4x

According to question,

3x = 12

⇒ x = 4

∴ Required days = 4x = 4 × 4 = 16 days.

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