Profit and Loss Question 3 - CAT 2021
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:
Step-by-Step Explanation
Let the total investment in the business be T.
Profit distribution directly mirrors investment distribution. Anil owns a 70% share of the total investment, so he receives 70% of any profit generated.
Analyze Anil's Shift:
When the overall profit rate drops from 18% to 15%, the drop in total profit corresponds to 3% of the total investment (T).
Anil’s share of this loss is ₹ 420:
70% of 3% of T = 420
0.70 × 0.03 × T = 420
0.021T = 420
T = 420 / 0.021 = ₹ 20000
The total investment made by all three partners combined is ₹ 20000.
Analyze Chintu's Shift:
When the overall profit rate rises from 15% to 17%, the total profit increases by 2% of T.
Total Profit Increase = 2% of 20000 = ₹ 400
Chintu's personal profit allocation increases by ₹ 80 out of this ₹ 400 total increase.
Chintu's Investment Share = 80 / 400 = 20%
Determine Bobby's Share:
Bobby's Share = 100% − Anil's Share + Chintu's Share
Bobby's Share = 100% − 70% + 20% = 10%
Bobby's Investment Amount = 10% of 20000 = ₹ 2000
Correct Option: A
💡 FundaMakers Tip:
Think in absolute shifts rather than deep formulas.
If a 70% stakeholder loses ₹ 420 from a market drop, the total loss across the entire business must be:
420 / 0.70 = ₹ 600.
Because this ₹ 600 drop represents a 3% change in the company's total yield (18% − 15%), you can immediately deduce that a 1% yield equals ₹ 200, which sets the total capital base at ₹ 20000. Scaling the changes step-by-step keeps your arithmetic clean.