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 Rs. $420$ if the overall profit goes down from $18\%$ to $15\%$. Chintu's share of profit increases by Rs. $80$ if the overall profit goes up from $15\%$ to $17\%$. The amount, in INR, invested by Bobby is

This is a partnership problem where three people invest money together and share profits proportionally based on their investments.

In partnerships, if someone invests 30% of total money, they get 30% of total profit. The profit percentage affects everyone's absolute profit amount, but their share ratio stays the same.

---

Anil invests 70% of total investment. When profit rate drops from 18% to 15%, Anil's profit decreases by Rs. 420.

Let total investment = T, then:

Anil's investment = 0.7T

When profit rate is 18%: Anil gets $0.7 \times (18\% \text{ of } T) = 0.7 \times 0.18T$

When profit rate is 15%: Anil gets $0.7 \times (15\% \text{ of } T) = 0.7 \times 0.15T$

The decrease in Anil's profit:

$0.7 \times 0.18T - 0.7 \times 0.15T = 0.7T \times (0.18 - 0.15) = 0.7T \times 0.03 = 420$

$0.7 \times 0.03 \times T = 420$

$0.021T = 420$

$T = 420 \div 0.021 = \text{Rs. } 20000$

---

Chintu's profit increases by Rs. 80 when profit rate increases from 15% to 17%.

Let Chintu's investment = C

Since Chintu's share = $\tfrac{C}{T} \times$ Total Profit:

At 15% profit rate: Chintu gets $\tfrac{C}{20000} \times (15\% \text{ of } 20000) = C \times 0.15$

At 17% profit rate: Chintu gets $\tfrac{C}{20000} \times (17\% \text{ of } 20000) = C \times 0.17$

The increase in Chintu's profit:

$C \times 0.17 - C \times 0.15 = C \times (0.17 - 0.15) = C \times 0.02 = 80$

$0.02C = 80$

$C = 80 \div 0.02 = \text{Rs. } 4000$

---

Total investment = Rs. 20000

Anil's investment = 70% of 20000 = Rs. 14000

Chintu's investment = Rs. 4000

Bobby's investment = Total - Anil's - Chintu's = 20000 - 14000 - 4000 = Rs. 2000

---

Bobby invested Rs. 2000

In partnership problems, profit sharing ratio equals investment ratio. We use the given changes in profit to find unknown values and always verify that all investments add up to the total.