Question

From a bank, Ram and Shyam together took loans under simple interest and lent the total to Mohan at \(2%\) higher} simple interest. After \(4\) years, Ram’s total money earned (after paying the bank interest) was \(\rupee 400\) more than Shyam’s. By how much was the amount borrowed by Ram more than that borrowed by Shyam?

• A. 10000
• B. 20000
• C. 5000
• D. 250000

Hint:

In simple-interest “lend at a higher rate” problems, the profit depends only on the rate difference} and time. The profit difference between two investors is \((\text{rate diff} \times \text{time})\) times the difference of their principals.

Answer 1

The Correct Option is C

Solution:
Step 1 (Set up principals and rates).
Let Ram and Shyam borrow \(\,R\) and \(\,S\) rupees, respectively, from the bank at \(r%\) p.a. (simple interest). They together lend to Mohan at \((r+2)%\) p.a. (simple interest). Step 2 (Net gain per person).
For each person, interest received} minus interest paid} each year \(=\) \( (r+2)-r = 2%\) of their own principal. Over \(4\) years, net gain rate \(= 2%\times 4 = 8%\). Thus Ram’s gain \(=0.08R\) and Shyam’s gain \(=0.08S\). Step 3 (Use the gain difference).
Given Ram’s gain exceeds Shyam’s by \(\rupee 400\): \[ 0.08R - 0.08S = 400 \ \ 0.08(R-S)=400 \ \ R-S=\frac{400}{0.08}=5000. \] \[ {\rupee 5000 \ \text{(Option (c)}} \]