15 kg of ₹10 per kg wheat is mixed with 5 kg of another type of wheat to get a mixture costing ₹30 per kg. Find the price (per kg) of the costlier wheat.

Correct — A. Price the whole mixture, then subtract the cheap part.

Mixture = 15 + 5 = 20 kg at ₹30 per kg
Total cost = 20 × 30 = ₹600
Cheap wheat = 15 × 10 = ₹150
So 5 kg of the costlier wheat cost 600 − 150 = ₹450

Rate = 450 ⁄ 5 = ₹90 per kg → option (a)

Why the others are wrong

• (b)
  ₹70 — Plug it back: 150 + 5 × 70 = ₹500 for 20 kg, which is ₹25 per kg, not ₹30. Every rupee below ₹90 leaves the mixture cheaper than the question states.
• (c)
  ₹60 — ₹60 gives 150 + 300 = ₹450 for 20 kg, or ₹22.50 per kg. It is roughly twice the mean rate, the answer of someone doubling ₹30 rather than balancing the two costs.
• (d)
  ₹80 — ₹80 is what you get by charging 20 kg at ₹10 (₹200) instead of 15 kg, leaving 600 − 200 = ₹400 for 5 kg. Only 15 kg of the cheap wheat went in.

A mixture question is one equation: the cost of the parts equals the cost of the whole.

Write it as 15(10) + 5(x) = 20(30). Nothing about mixing is special — the mean rate is just the total money divided by the total weight.

Alligation is the same statement rearranged: the ratio of the quantities, 15 : 5 = 3 : 1, is the inverse ratio of the distances from the mean, (x − 30) : (30 − 10), which gives x − 30 = 60.

Key facts

• Total cost of a mixture equals the sum of the costs of its ingredients.
• 15 kg at ₹10 and 5 kg at ₹90 make 20 kg costing ₹600, which is ₹30 per kg.
• By alligation the quantity ratio 3 : 1 forces the dearer rate to sit three times as far above the mean as the cheaper rate sits below it.

Common traps

• Averaging ₹10 and the unknown rate as if the two quantities were equal.
• Using the full 20 kg at the cheaper rate when only 15 kg is cheap.
• Reading ₹30 as the total cost rather than the rate per kilogram.

No directly related past PYQ was found.