Find the present worth (PW) and the true discount reckoning `6%` per annum simple interest of Rs. 176 due in 20 months time-

Options

A. Rs. 160, Rs. 16
B. Rs. 130, Rs. 46
C. Rs. 150, Rs. 26
D. None of these

Answer

To solve the problem of finding the present worth (PW) and the true discount of Rs. 176 due in 20 months at a simple interest rate of 6% per annum, we can follow these steps:

### Step 1: Identify the given values
- Amount (A) = Rs. 176
- Rate (R) = 6% per annum
- Time (T) = 20 months

### Step 2: Convert time from months to years
Since the rate is per annum, we need to convert the time into years.
\[ T = \frac{20 \text{ months}}{12} = \frac{20}{12} = \frac{5}{3} \text{ years} \]

### Step 3: Use the formula for Present Worth (PW)
The formula for Present Worth is:
\[ PW = \frac{100 \times A}{100 + (R \times T)} \]
Substituting the values we have:
\[ PW = \frac{100 \times 176}{100 + (6 \times \frac{5}{3})} \]

### Step 4: Calculate the denominator
First, calculate \( R \times T \):
\[ R \times T = 6 \times \frac{5}{3} = 10 \]
Now, substitute this back into the denominator:
\[ 100 + (R \times T) = 100 + 10 = 110 \]

### Step 5: Substitute back to find PW
Now substitute the values into the PW formula:
\[ PW = \frac{100 \times 176}{110} = \frac{17600}{110} \]

### Step 6: Simplify the fraction
Now, simplify \( \frac{17600}{110} \):
\[ PW = \frac{17600 \div 110}{110 \div 110} = \frac{160}{1} = 160 \]

### Step 7: Calculate the True Discount (TD)
The formula for True Discount is:
\[ TD = A - PW \]
Substituting the values we have:
\[ TD = 176 - 160 = 16 \]

### Final Answers
- Present Worth (PW) = Rs. 160
- True Discount (TD) = Rs. 16

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