CAT 2021 Set-2 | Quantitative Aptitude | Question: 2

Question

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, $\text{in INR},$ invested by Bobby is

• A. $2400$
• B. $2200$
• C. $2000$
• D. $1800$

Answer 1

Let the total amount invested by Anil, Bobby, and Chintu be $\text{‘I’}.$

Anil’s share of investment is $70\%.$ His share of profit decreases by ₹$ \; 420$ if the overall profit goes down from $18 \%$ to $15\%.$

Now, $70 \% \; \text{of} \; (18\% \; \text{of I} – 15\% \; \text{of I}) = 420$

$\Rightarrow 70 \% \; \text{of} \; 3\% \; \text{of I} = 420$

$\Rightarrow \frac{70}{100} \times \frac{3}{100} \times \text{I} = 420$

$\Rightarrow \boxed{\text{I} = 20000}$

Chintu’s share of profit increases by ₹$ \;80$ if the overall profit goes up from $15 \%$ to $17\%.$

Let the percentage share of Chintu be $\text{‘C’}.$

$\text{C} \% \; \text{of} \; 2\% \; \text{of I} = 80$

$\Rightarrow \frac{\text{C}}{100} \times \frac{2}{100} \times 20000 = 80$

$\Rightarrow \boxed{\text{C} = 20\%}$

Now, profit share by Bobby $ = 100\% – (70\% + 20\%)= 100\% – 90\% = 10\%$

$\therefore$ The amount invested by Bobby $ = 10\% \; \text{of I} = \dfrac{10}{100} \times 20000 =$ ₹ $\; 2000.$

Correct Answer $: \text{C}$