The simple interest and true discount on a certain sum for a give time and given rate are Rs 85 and Rs 80 the sum due is.

Options

A. a)Rs 1300
B. b)Rs 1370
C. c)Rs 1400
D. d)Rs 1360

Answer

To solve the problem step by step, we need to find the sum due given the simple interest (SI) and the true discount (TD).

### Step 1: Understand the relationship between Simple Interest and True Discount
The formula for True Discount (TD) is:
\[ \text{TD} = \text{SI} \times \frac{\text{TD}}{\text{SI} - \text{TD}} \]

### Step 2: Identify the values given in the problem
From the problem, we have:
- Simple Interest (SI) = Rs 85
- True Discount (TD) = Rs 80

### Step 3: Use the formula to find the Principal (P)
We can rearrange the formula to find the Principal (P):
\[ P = \frac{\text{SI} \times \text{TD}}{\text{SI} - \text{TD}} \]

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ P = \frac{85 \times 80}{85 - 80} \]

### Step 5: Calculate the denominator
Calculate \( 85 - 80 \):
\[ 85 - 80 = 5 \]

### Step 6: Calculate the numerator
Now calculate \( 85 \times 80 \):
\[ 85 \times 80 = 6800 \]

### Step 7: Divide the numerator by the denominator
Now divide \( 6800 \) by \( 5 \):
\[ P = \frac{6800}{5} = 1360 \]

### Step 8: Find the sum due
The sum due (S) is the Principal plus the Simple Interest:
\[ S = P + \text{SI} = 1360 + 85 = 1445 \]

### Final Answer
The sum due is Rs 1445.

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