A person invested a certain sum of money at 6% per annum simple interest and another sum at 8% per annum simple interest at the same time. After 4 years, he received interest ₹1,560 from both sums. One-fifth of the first sum is equal to one-sixth of the second sum. Find the total sum invested.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. ₹5,500.
Let first sum = x, second sum = y.
Given: x/5 = y/6 → 6x = 5y → y = (6x)/5
Interest after 4 years: (6% of x × 4) + (8% of y × 4) = 1560
=> (24x/100) + (32y/100) = 1560
Multiply by 100: 24x + 32y = 156000
Substitute y: 24x + 32 × (6x/5) = 156000
24x + (192x/5) = 156000
Multiply by 5: 120x + 192x = 780000
312x = 780000
x = 2500
y = (6 × 2500)/5 = 3000
Total = 2500 + 3000 = ₹5500