₹10,000 is lent partly at 8% and partly at 12% simple interest. The total interest for one year is ₹960. How much was lent at each rate?

Alligation works for anything that is a weighted average: prices, speeds, marks, interest rates. Two loans at 8% and 12% blend to an average rate somewhere in between. The average 9.6% is closer to 8%, so more money must be at 8%. Find the ratio, then split ₹10,000.

Question: ₹10,000 split between 8% and 12%; total interest ₹960 for one year.

1. Average rate = 960 / 10,000 x 100 = 9.6%.
2. Alligation:

• At 8% : at 12% = (12 - 9.6) : (9.6 - 8) = 2.4 : 1.6 = 3 : 2.

1. At 8% = 10,000 x 3/5 = ₹6,000. At 12% = ₹4,000.

Check: 8% of 6,000 = 480, 12% of 4,000 = 480. Total ₹960.

Equation method: 0.08x + 0.12(10,000 - x) = 960 gives 1,200 - 0.04x = 960, so x = 6,000.

const x = (1200 - 960) / 0.04;
console.log(Math.round(x)); // Output: 6000
console.log(Math.round(0.08 * 6000 + 0.12 * 4000)); // Output: 960

• Getting the ratio reversed and putting more money at 12%.
• Forgetting to turn ₹960 into a rate before using alligation.