Kiran lent ₹4,000 to two persons such that one part of it at the rate of 8% per annum and the remaining part at the rate of 10% per annum. He got an annual simple interest of ₹352. Then the sum lent at 10% is:

Correct — C. Let ₹x be the part lent at 10%, so ₹(4000 − x) is lent at 8%.

0.10x + 0.08(4000 − x) = 352
0.10x + 320 − 0.08x = 352
0.02x = 32
x = 32⁄0.02 = ₹1,600 → option (c)

Check: ₹1,600 at 10% earns ₹160 and ₹2,400 at 8% earns ₹192, together ₹352.

Why the others are wrong

• (a)
  ₹2,400 — ₹2,400 is the part lent at 8%, the other half of the same split. Reverse the roles and the interest comes to 240 + 128 = ₹368, not ₹352.
• (b)
  ₹1,800 — ₹1,800 at 10% with ₹2,200 at 8% yields 180 + 176 = ₹356, four rupees more than the interest stated.
• (d)
  ₹2,200 — ₹2,200 at 10% with ₹1,800 at 8% yields 220 + 144 = ₹364, twelve rupees over the ₹352 given.

One year of simple interest on a split sum is a weighted-average problem. The whole ₹4,000 earned ₹352, so the blended rate is 352⁄4000 = 8.8% per annum.

Alligation puts 8.8 between 8 and 10 and reads the ratio of the two parts as (10 − 8.8) : (8.8 − 8) = 1.2 : 0.8 = 3 : 2, the first term belonging to the 8% part.

So the 10% part is 2⁄5 of ₹4,000 = ₹1,600. The equation and the alligation are the same arithmetic, and alligation is faster once the blended rate comes out clean.

Key facts

• Simple interest for one year is the rate multiplied by the principal.
• The blended rate here is 352⁄4000 = 8.8% per annum.
• Alligation gives the two parts in the ratio (10 − 8.8) : (8.8 − 8) = 3 : 2.
• That ratio splits ₹4,000 into ₹2,400 at 8% and ₹1,600 at 10%.

Common traps

• Solving correctly and then reporting ₹2,400 because the variable was set up on the 8% side.
• Handing the larger share to the higher rate — alligation gives the larger share to the rate nearer the blended value, which is 8% here.

No directly related past PYQ was found.