Time and Work with Leaving Early

CMAT 2026 · Quantitative Techniques & Data Interpretation · Medium · Time and Work

Raman can do a piece of work in 16 days. Satish can do the same work in 8 days while Ashok can do it in 32 days. All of them worked together when they started, but Satish left after 2 days. Raman left 3 days before the completion of work. How long did it take to complete the entire work?

  1. A.

    8 days

  2. B.

    10 days

  3. C.

    12 days

  4. D.

    14 days

Answer

B

Explanation

Total work = LCM(16, 8, 32) = 32 units. Efficiencies: Raman = 2, Satish = 4, Ashok = 1. Let total time taken be XX days. Satish worked for 2 days, Raman worked for X−3X-3 days, Ashok worked for XX days. Work done: 4×2+2(X−3)+1(X)=32  ⟹  8+2X−6+X=32  ⟹  3X+2=32  ⟹  X=104 \times 2 + 2(X - 3) + 1(X) = 32 \implies 8 + 2X - 6 + X = 32 \implies 3X + 2 = 32 \implies X = 10 days.

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