CSAT Solved Papers/ 2021/Q80

2021 CSAT — Q80

Quant Arithmetic & numeracy 2.5 marks Medium

A man completes 78\tfrac{7}{8} of a job in 2121 days. How many more days will it take him to finish the job if quantum of work is further increased by 50%50\%?

  1. A 24
  2. B 21
  3. C 18
  4. D 15 Answer

Worked rationale

Take the original job as 11 unit. He does 78\tfrac78 in 2121 days, so his rate is

7/821=7168=124 job-units per day.\frac{7/8}{21} = \frac{7}{168} = \frac{1}{24}\ \text{job-units per day}.

The total work is increased by 50%50\% to 1.51.5 units. He has already done 78=0.875\tfrac78 = 0.875 unit, so the remaining work is

1.5−0.875=0.625=58 unit.1.5 - 0.875 = 0.625 = \tfrac58\ \text{unit}.

Days needed at 124\tfrac{1}{24} per day:

5/81/24=58×24=15 days.\frac{5/8}{1/24} = \frac58 \times 24 = 15\ \text{days}.

Answer: (d) 15.

Why the other options miss

  • A
    timed the whole job, not the remainder: computes the days for the whole increased job (1.51.5 units) from scratch instead of the remaining work.
  • B
    reused the original figure: keeps the 2121 days, ignoring that only 58\tfrac58 remains.
  • C
    applied the increase to the wrong base: puts the 50%50\% on the remaining 18\tfrac18 rather than the total job, getting the wrong leftover.

Specialist insight

Pin the rate first (78\tfrac78 in 2121 days ⇒124\Rightarrow \tfrac{1}{24}/day), then compute the new remaining work against the enlarged total: 1.5−0.875=581.5 - 0.875 = \tfrac58. The ”50%50\% increase” applies to the whole job, not the unfinished part — that’s the trap behind (c). Remaining-work problems are always (new total −- done) ÷\div rate; keep the base of every fraction explicit.

The trap, in one line

Rate =124=\tfrac1{24}/day; remaining =1.5−78=58=1.5-\tfrac78=\tfrac58; days =58×24=15⇒=\tfrac58\times24 = 15 \Rightarrow (d).

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