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SSC MTS 2022 PYQ — Question 51

SSC MTS - 26 July 2022 - Shift 2 • Quantitative Aptitude • Q51

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Kajal can do a piece of work alone in 24 days, while Neha can do the same work alone in 40 days. Kajal started the work alone, and then after 12 days, Neha joined her till the completion of the work. How long did the work take to be completed since Kajal started to work on it?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. (39/2) days

Let the total work to be be W - 

So,

Work done by Kajal in 24 days = W

Work done by Kajal in 1 day = W/24

Now,

Work done by Neha in 40 days = W

Work done by Neha in 1 day = W/40

Now,

Work done by Kajal in 12 days = W24×12\frac{W}{24}\times12  = W2\frac{W}{2}

So,

Work remaining = W−W2W-\frac{W}{2} = W2\frac{W}{2}

Now,

Work done by Kajal and Neha together in 1 day = W24+W40\frac{W}{24}+\frac{W}{40} = (5W+3W120)\left ( \frac{5W+3W}{120} \right )= W15\frac{W}{15}

Time taken by Kajal and Neha to complete W2\frac{W}{2} work = W2W15\frac{\frac{W}{2}}{\frac{W}{15}}= 152\frac{15}{2} days

So,

Total time taken to complete the work = 12+15212+\frac{15}{2}= 392\frac{39}{2} days.