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Question:

Three Professors Dr. Gupta, Dr. Sharma and Dr. Singh are evaluating answer scripts of a subject. Dr. Gupta is 40% more efficient than Dr. Sharma, who is 20% more efficient than Dr. Singh. Dr. Gupta takes 10 days less than Dr. Sharma to complete the evaluation work. Dr. Gupta starts the evaluation work and works for 10 days and then Dr. Sharma takes over. Dr. Sharma evaluates for next 15 days and then stops. In how many days, Dr. Singh can complete the remaining evaluation work.

Explanation:

Let Dr. Gupta take x days to complete the evaluation work.

∴ Dr. Sharma takes x + 10 days

As Dr. Gupta is 40% more efficient than Dr. Sharma, we have

$\frac{1}{x}$ = $\frac{1.4}{x+10}$

∴ x = 25

∴ x + 10 = 35

Also, Dr. Sharma is 20% more efficient than Dr. Singh.

∴ If  Dr. Singh takes y days to complete the evaluation work,

$\frac{1}{35}$ = $\frac{1.2}{y}$

∴ y = 42

Now, let Dr. Singh complete the evaluation work in n days after Dr. Gupta has worked for 10 days and Dr. Sharma has worked for 15 days.

∴ $\frac{10}{25}$ + $\frac{15}{35}$ + $\frac{n}{42}$ = 1

∴ n = 7.2

Hence, option (a).