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CAT 2017 Slot 2 — QA Question 13

PaymentsEasy

Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal’s share, in rupees, is

Answer & solution

Correct answer: 100

  • 100

  • B

    200

  • C

    300

  • D

    400

Solution

Easy

Wages are split in proportion to work done. Find each person's one-day rate, get Kamal's rate as the leftover after Amal and Bimal, then take Kamal's fraction of the total job to split the Rs 1000.

1

Combined and individual rates. All three together finish in 4 days, so their combined daily rate is the reciprocal of 4. Amal and Bimal's daily rates are reciprocals of 10 and 8.

(A+B+K)=14(together, 4 days)A+B=110+18=4+540=940(given rates)\begin{aligned} &\text{(A+B+K)} = \tfrac14 \quad\text{(together, 4 days)}\\ &A+B = \tfrac{1}{10}+\tfrac18 = \tfrac{4+5}{40} = \tfrac{9}{40} \quad\text{(given rates)} \end{aligned}
2

Kamal's daily rate. Subtract Amal+Bimal from the combined rate.

K=14−940=10−940=140(from step 1)\begin{aligned} &K = \tfrac14 - \tfrac{9}{40} = \tfrac{10-9}{40} = \tfrac{1}{40} \quad\text{(from step 1)} \end{aligned}
3

Kamal's share of the job. The job runs for 4 days, so Kamal's fraction of the whole work is his rate times 4.

Kamal’s work=4×140=110(of the job)\begin{aligned} &\text{Kamal's work} = 4 \times \tfrac{1}{40} = \tfrac{1}{10} \quad\text{(of the job)} \end{aligned}
4

Kamal's pay. Take that fraction of the total Rs 1000.

Share=110×1000=100\begin{aligned} &\text{Share} = \tfrac{1}{10}\times 1000 = 100 \end{aligned}
Kamal’s share=Rs 100\text{Kamal's share} = \text{Rs } 100

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CAT 2017 Slot 2 QA Q13: Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complet — Solution | TheCATExam