A and B together can do a piece of work in 24 days B and C together can do it in 36 days If A is thr...........

Quantitative Aptitude (MTS) Time & distance

A and B together can do a piece of work in 24 days. B and C together can do it in 36 days. If A is thrice as good a workman as C.

in how many days can B alone do the work?

This questions was previously asked in

SSC MTS 13th October 2021 Shift-3

48 days

36 days

45 days

40 days

- Let's define the work rates:

- Let C's 1 day's work be \( x \).

- Then, A's 1 day's work is \( 3x \) (since A is thrice as good as C).

- From A and B together can do work in 24 days:

- \( (3x + B's \ rate) \times 24 = 1 \)

- From B and C together can do work in 36 days:

- \( (B's \ rate + x) \times 36 = 1 \)

- On solving these, we get A does \(\frac{1}{32}\) of work/day and C does \(\frac{1}{96}\).

- Hence, B's rate is \(\frac{1}{48}\); B alone takes 48 days.

- Correct Answer: Option 1: 48 days.

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