How many approximate kgs of sugar costing ₹45 per kg must be mixed with 25 kg of sugar costing ₹32 per kg so that a 15% gain may be obtained by selling the mixture at ₹43.70 per kg?

Correct — C. Find what the mixture must cost, then balance the two sugars around that price.

Cost price of mixture = selling price ÷ 1.15
= 43.70 ÷ 1.15 = ₹38 per kg

Alligation, ₹32 sugar : ₹45 sugar = (45 − 38) : (38 − 32) = 7 : 6
₹45 sugar needed = 25 × 6⁄7 = 150⁄7 ≈ 21.4 kg
Nearest option: 21 kg → option (c)

Why the others are wrong

• (a)
  15 kg — With 15 kg the mixture costs (675 + 800) ÷ 40 = ₹36.875 per kg, so selling at ₹43.70 gives about an 18.5% gain, not 15%.
• (b)
  25 kg — Equal 25 kg lots cost (45 + 32) ÷ 2 = ₹38.50 per kg on average, and ₹43.70 on that is only about a 13.5% gain, not 15%.
• (d)
  18 kg — With 18 kg the mixture costs (810 + 800) ÷ 43 ≈ ₹37.44 per kg, so selling at ₹43.70 gives about a 16.7% gain, not 15%.

A gain is a percentage of cost price, so the mixture's cost comes from dividing ₹43.70 by 1.15, not from taking 15% off it.

Alligation then balances the two prices around that ₹38 mean. The ₹45 sugar sits ₹7 above it and the ₹32 sugar ₹6 below, so the cheaper sugar takes the larger share, 7 parts to 6.

One equation gives the same result: 45x + 800 = 38(x + 25), so 7x = 150.

Key facts

• Cost price = selling price ÷ (1 + gain ⁄ 100), so ₹43.70 at a 15% gain means a cost of ₹38.
• Alligation: cheaper quantity : dearer quantity = (dearer price − mean) : (mean − cheaper price).
• Here that ratio is (45 − 38) : (38 − 32) = 7 : 6, so 25 kg of the ₹32 sugar pairs with 150⁄7 ≈ 21.4 kg of the ₹45 sugar.

Common traps

• Taking 15% off ₹43.70 to get ₹37.145. The gain is measured on cost, so cost = 43.70 ÷ 1.15 = ₹38.
• Writing the alligation ratio the wrong way round: 6 : 7 gives 25 × 7⁄6 ≈ 29.2 kg, which is not among the options.

No directly related past PYQ was found.