7. If Shivam and Dharam invested their respective amounts in a partnership for 9 months and 12 months

respectively and total prot after the end of 12 months is Rs.37200, then nd prot share of Dharam.

(a) Rs.21,600 (b) Rs.28,800 (c) Rs.24,000 (d) Rs.19,200

8. If Harish invested his amount across two schemes for 3 years – one scheme oering 15% p.a. at SI and other

one oering 18% p.a. at SI and he received total interest of Rs.16,650 from both schemes together, then nd

amount invested by Harish at 15% p.a.

(a) Rs.13,000 (b) Rs.16,000 (c) Rs.15,000 (d) Rs.20,000

9. If Deepak invested a fraction of his amount at 16% p.a. for 5 years at SI and total interest received by him

from his investment is Rs.12,800, then nd amount invested by Deepak is what percent of amount of Dharam?

(a) 50% (b) 66 2/3 % (c) 100% (d) 33 2/3 %

10. Find average of amount of Deepak, Dharam, Shivam, Harish and Ankit.

(a) Rs.37,000 (b) Rs.37,600 (c) Rs.38,200 (d) Rs.36,400

Let's go through each of these questions step by step.

### Question 7: Profit Share of Dharam

Given:
- **Shivam's amount** \( S = 30000 \)
- **Dharam's amount** \( D = 24000 \)
- Shivam's investment period = 9 months
- Dharam's investment period = 12 months
- Total profit = Rs. 37,200

The ratio of their profits is proportional to the product of their investments and the time period they invested:

\[
\text{Ratio of profits} = \frac{S \times 9}{D \times 12} = \frac{30000 \times 9}{24000 \times 12} = \frac{270000}{288000} = \frac{45}{48} = \frac{15}{16}
\]

So, the ratio of their profit shares is \( 15:16 \).

Let's denote Shivam's profit as \( 15x \) and Dharam's profit as \( 16x \).

Total profit:
\[
15x + 16x = 31x = 37200
\]

Solving for \( x \):
\[
x = \frac{37200}{31} = 1200
\]

Dharam's profit share:
\[
16x = 16 \times 1200 = 19200
\]

**Correct Answer:** (d) Rs. 19,200

### Question 8: Amount Invested by Harish at 15% p.a.

Given:
- Harish's total amount \( H = 33000 \)
- Let \( x \) be the amount invested at 15% p.a.
- Then, \( 33000 - x \) is the amount invested at 18% p.a.
- The total interest received over 3 years = Rs. 16,650

Interest from the 15% scheme:
\[
\text{Interest at 15%} = \frac{15 \times x \times 3}{100} = 0.45x
\]

Interest from the 18% scheme:
\[
\text{Interest at 18%} = \frac{18 \times (33000 - x) \times 3}{100} = 0.54(33000 - x)
\]

Total interest:
\[
0.45x + 0.54(33000 - x) = 16650
\]

Expanding and simplifying:
\[
0.45x + 17820 - 0.54x = 16650
\]
\[
-0.09x = -1170
\]
\[
x = \frac{1170}{0.09} = 13000
\]

**Correct Answer:** (a) Rs. 13,000

### Question 9: Amount Invested by Deepak as a Percentage of Dharam's Amount

Given:
- Deepak's amount \( Dp = 18000 \)
- Simple interest \( SI = 12800 \)
- Rate \( r = 16\% \)
- Time \( t = 5 \) years

Simple Interest formula:
\[
SI = \frac{P \times r \times t}{100}
\]
Substituting the values:
\[
12800 = \frac{P \times 16 \times 5}{100} = 0.8P
\]

Solving for \( P \):
\[
P = \frac{12800}{0.8} = 16000
\]

Now, we need to find the percentage of this amount relative to Dharam's amount:
\[
\text{Percentage} = \frac{16000}{24000} \times 100 = \frac{2}{3} \times 100 = 66.67\%
\]

**Correct Answer:** (b) 66 2/3 %

### Question 10: Average of Amounts of Deepak, Dharam, Shivam, Harish, and Ankit

The amounts are:
- Shivam: \( S = 30000 \)
- Deepak: \( Dp = 18000 \)
- Dharam: \( D = 24000 \)
- Harish: \( H = 33000 \)
- Ankit: \( A = 77000 \)

Total sum of amounts:
\[
30000 + 18000 + 24000 + 33000 + 77000 = 182000
\]

Average:
\[
\text{Average} = \frac{182000}{5} = 36400
\]

**Correct Answer:** (d) Rs. 36,400

---

If you have more questions or need further clarification on any step, feel free to ask! Here are 5 related questions to explore:

1. What would happen if the interest rates on both schemes for Harish were swapped?
2. How much more would Dharam's profit share be if he invested for 15 months instead of 12?
3. How would Ankit's average amount affect the total if he received an additional Rs. 10,000 bonus?
4. What percentage of Deepak's amount is equivalent to Harish's additional Rs. 3000?
5. If the interest rate on Ankit's investment was 25% instead of 20%, how much interest would he receive?

**Tip:** Always verify calculations, especially with ratios and percentages, to avoid common mistakes.

Explore solutions to mathematical problems involving profit sharing, simple interest calculations, and percentage calculations. Includes detailed steps for questions related to investment periods, profit shares, interest rates, and averages. Perfect for high school students preparing for exams.

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