There are 5 persons – Deepak, Shivam, Dharam, Harish & Ankit. Amount of Deepak is 40% less than amount of
Shivam. Amount of Dharam is equal to average of amount of Deepak and Shivam. Harish amount is Rs.3000
more than Shivam’s amount. Ratio of amount of Ankit to that of Harish is 7 : 3 and Harish’s amount is 137.5%
of Dharam’s amount.
6. If Ankit invested his amount in a scheme oering 20% p.a. at CI for 2 years, then nd interest received by Ankit
from the scheme.
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(a) Rs.13,200 (b) Rs.7,920 (c) Rs.33,880 (d) Rs.10,560
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 solve the problem step by step.

### Step 1: Define Variables for Each Person's Amount
- Let Shivam's amount be \( S \).
- Deepak's amount is \( 0.6S \) (since it is 40% less than Shivam's).
- Dharam's amount is \( D = \frac{S + 0.6S}{2} = 0.8S \).
- Harish's amount is \( H = S + 3000 \).
- Ankit's amount is \( A \), and the ratio of Ankit to Harish's amount is \( \frac{A}{H} = \frac{7}{3} \).

We are also given that Harish's amount is 137.5% of Dharam's amount:
\[
H = 1.375 \times D = 1.375 \times 0.8S = 1.1S
\]

Since \( H = S + 3000 \), equating both expressions for \( H \):
\[
S + 3000 = 1.1S
\]
\[
0.1S = 3000
\]
\[
S = 30000
\]

### Step 2: Calculate the Amounts for Each Person
- **Shivam's amount** \( S = 30000 \)
- **Deepak's amount** \( 0.6S = 0.6 \times 30000 = 18000 \)
- **Dharam's amount** \( 0.8S = 0.8 \times 30000 = 24000 \)
- **Harish's amount** \( H = S + 3000 = 30000 + 3000 = 33000 \)
- **Ankit's amount**:
\[
\frac{A}{33000} = \frac{7}{3} \Rightarrow A = \frac{7}{3} \times 33000 = 77000
\]

### Step 3: Solve the Questions

**Question 6: Compound Interest for Ankit's Investment**
- Ankit invested his amount \( A = 77000 \) at 20% p.a. compounded annually for 2 years.
  
  The compound interest formula:
  \[
  CI = A \times \left(1 + \frac{r}{100}\right)^n - A
  \]
  Where:
  - \( A = 77000 \)
  - \( r = 20 \% \)
  - \( n = 2 \) years

  \[
  CI = 77000 \times \left(1 + \frac{20}{100}\right)^2 - 77000
  \]
  \[
  CI = 77000 \times \left(1.2\right)^2 - 77000 = 77000 \times 1.44 - 77000 = 110880 - 77000 = 33880
  \]

  **Answer:** (c) Rs. 33,880

**Question 7: Profit Share of Dharam**
- Shivam's time of investment: 9 months
- Dharam's time of investment: 12 months
- Profit ratio \( \text{Shivam} : \text{Dharam} = 30000 \times 9 : 24000 \times 12 = 270000 : 288000 = 45 : 48 \)

  Total ratio = \( 45 + 48 = 93 \)
 

Explore detailed solutions to mathematical problems from a classroom practice paper, covering topics such as compound interest, profit sharing, and percentage calculations. Includes step-by-step explanations and answers to questions about investments and profits.

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