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Arithmetic/Time and Work

Question

MCQ} A and B together can finish a project in 2020 days. B alone takes 4545 days to finish the project. They start the project together, but A leaves after some days; B alone then takes a further 21.621.6 days to complete the remaining work. The number of days A alone would take to complete the project is:

Options

A

3030

B

3636

C

4545

D

6060

Answer

(B) 3636.

Detailed solution

Combined rate of A and B =1/20=1/20. B's rate =1/45=1/45.

So A's rate =1/201/45=(94)/180=5/180=1/36.=1/20 - 1/45 = (9-4)/180 = 5/180 = 1/36.

Therefore A alone takes 36\mathbf{36} days.

Consistency check with the third datum: Let A and B work together for tt days, then B alone for 21.621.6 days. Total work: t/20+21.6/45=1t/20=10.48=0.52t=10.4t/20 + 21.6/45 = 1 \Rightarrow t/20 = 1 - 0.48 = 0.52 \Rightarrow t = 10.4 days. Consistent.

Why this is CAT-level: The redundant ``21.621.6 days'' datum tempts students into setting up a two-variable equation system. The elegant route uses only the first two facts, with the third merely confirming consistency. Method selection -- not method execution -- is what saves time.

Answer: (B) 3636.