The ratio of the monthly salary of Om to that of Pihu is `7:9`. Om and Pihu both save `20%` and `40%` of their respective monthly salary respectively. Om invests `1/2`of his savings in PPF and Pihu invests `7/9` of his savings in PPF. If Om and Pihu together saved ₹17500 in PPF, what is Pihu's monthly salary?

Options

A. 72000
B. 36000
C. 45000
D. 35000

Answer

To solve the problem step by step, we will first denote the monthly salaries of Om and Pihu based on the given ratio, and then calculate their savings and investments.

### Step 1: Define the Salaries
Let the monthly salary of Om be \( 7x \) and the monthly salary of Pihu be \( 9x \), where \( x \) is a common multiplier.

### Step 2: Calculate Savings
- Om saves \( 20\% \) of his salary:
\[ \text{Savings of Om} = 20\% \text{ of } 7x = \frac{20}{100} \times 7x = \frac{7x}{5} \]

- Pihu saves \( 40\% \) of her salary:
\[ \text{Savings of Pihu} = 40\% \text{ of } 9x = \frac{40}{100} \times 9x = \frac{36x}{10} = \frac{18x}{5} \]

### Step 3: Calculate Investments in PPF
- Om invests \( \frac{1}{2} \) of his savings in PPF:
\[ \text{Investment of Om in PPF} = \frac{1}{2} \times \frac{7x}{5} = \frac{7x}{10} \]

- Pihu invests \( \frac{7}{9} \) of her savings in PPF:
\[ \text{Investment of Pihu in PPF} = \frac{7}{9} \times \frac{18x}{5} = \frac{126x}{45} = \frac{14x}{5} \]

### Step 4: Total Investment in PPF
According to the problem, the total amount saved in PPF by both Om and Pihu is ₹17500:
\[ \text{Total Investment in PPF} = \text{Investment of Om} + \text{Investment of Pihu} \]
\[ \frac{7x}{10} + \frac{14x}{5} = 17500 \]

### Step 5: Simplify the Equation
To add the fractions, we need a common denominator. The common denominator of 10 and 5 is 10:
\[ \frac{7x}{10} + \frac{28x}{10} = 17500 \]
\[ \frac{35x}{10} = 17500 \]
\[ 35x = 17500 \times 10 \]
\[ 35x = 175000 \]

### Step 6: Solve for x
\[ x = \frac{175000}{35} = 5000 \]

### Step 7: Calculate Pihu's Monthly Salary
Now that we have \( x \), we can find Pihu's monthly salary:
\[ \text{Pihu's Salary} = 9x = 9 \times 5000 = 45000 \]

### Final Answer
Pihu's monthly salary is ₹45000.

---