Three workers A B and C complete a given piece of work within different time spans while working ind...........

Quantitative Aptitude (RBI Grade B) Data Sufficiency

Directions : Each of the following questions is followed by three statements I, II and III. Find out whether the data given in each statement is sufficient to answer the questions.

Three workers A, B and C complete a given piece of work within different time spans while working individually. What is the ratio of efficiencies of C and B respectively?

I. A takes 100% more time than C to complete the given piece of work.

II. B completes the given piece of work within 8 days.

III. B takes 2 days less than A to complete the given piece of work.

This questions was previously asked in

RBI Grade B 2016

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Information in all three statements are not sufficient

All of the three

Only II and III

II and either only I or only III

Only I and III

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Explanation:

Correct option 2: All of the three

Above question can not be answered by taking any individual statement.

Lets try combinations

Combine statements:

From I & III:
A = 2C, B = A – 2 → B = 2C – 2.
We can’t find exact ratio because no absolute values are given → still insufficient.
From II & III:
B = 8, and B = A – 2 → A = 10.
But no info on C’s time → insufficient.
From I & II:
B = 8 days, A = 2C, but nothing linking A to B → insufficient.
From I, II, III together:
From II: B = 8 days
From III: A = 10 days
From I: A = 2C → 10 = 2C → C = 5 days
Ratio of efficiencies C:B = Time(B) / Time(C) = 8 / 5