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CAT 2021 Slot 2 — QA Question 14

PartnershipEasy

Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil’s share of investment is 70%. His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%. Chintu’s share of profit increases by ₹ 80 if the overall profit goes up from 15% to 17%. The amount, in INR, invested by Bobby is 

Answer & solution

  • 2000

  • B

    2400

  • C

    2200

  • D

    1800

Solution

Easy

Each partner's share of the overall profit is (their investment fraction) ×\times (overall profit). Since the profit is stated as a percentage of total investment II, a change in profit rate changes each share by (their fraction) ×\times (rate change) ×I\times I. Use Anil's change to find II, then Chintu's change to find Chintu's fraction, and Bobby's fraction is whatever is left.

1

Find total investment II from Anil's change. Profit rate drops 18%→15%18\%\to15\%, a fall of 3%3\% of II. Anil holds 70%70\%, so his share falls by 70%70\% of that, which equals 420420.

420=70100×3100×I⇒ 420=0.021 I⇒ I=20000\begin{aligned} &420=\frac{70}{100}\times\frac{3}{100}\times I\\ &\Rightarrow\ 420=0.021\,I\\ &\Rightarrow\ I=20000 \end{aligned}
2

Find Chintu's fraction c%c\%. Profit rate rises 15%→17%15\%\to17\%, a gain of 2%2\% of II. Chintu's share rises by c%c\% of that, which equals 8080.

80=c100×2100×20000⇒ 80=4c⇒ c=20\begin{aligned} &80=\frac{c}{100}\times\frac{2}{100}\times 20000\\ &\Rightarrow\ 80=4c\\ &\Rightarrow\ c=20 \end{aligned}
3

Bobby's investment. Shares sum to 100%100\%, so Bobby holds 100−70−20=10%100-70-20=10\% of II.

Bobby=10100×20000=2000\begin{aligned} &\text{Bobby}=\frac{10}{100}\times 20000=2000 \end{aligned}
Bobby invested INR 2000\text{Bobby invested } \mathrm{INR}\ 2000
CAT 2021 Slot 2 QA Q14: Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to the — Solution | TheCATExam