A man buys 10 kg of wheat at a rate of ₹26/kg. The wheat is mixed with 6 kg of other good quality of wheat to get a mixture at a price of ₹35/kg. The price of good quality wheat per kg (in ₹) is:

Correct — D. Price the whole mixture first, then subtract the part you already know.

Cost of the 10 kg at ₹26/kg = 10 × 26 = ₹260
Total mixture = 10 + 6 = 16 kg
Value of that mixture at ₹35/kg = 16 × 35 = ₹560
Cost of the 6 kg of good wheat = 560 − 260 = ₹300

Rate = 300 ⁄ 6 = ₹50 per kg → option (d).

Why the others are wrong

• (a)
  46 — At ₹46 the 6 kg would be worth 6 × 46 = ₹276, so the 16 kg would total ₹536 — that is ₹33.50/kg, not ₹35.
• (b)
  38 — At ₹38 the 6 kg comes to ₹228 and the mixture to ₹488, i.e. ₹30.50/kg. Too cheap to lift 10 kg of ₹26 wheat up to ₹35.
• (c)
  42 — At ₹42 the 6 kg is ₹252 and the whole 16 kg is ₹512, giving ₹32/kg. The gap of ₹3 per kg is exactly the ₹48 still missing.

A mixture question is a weighted average in disguise. The value of the whole equals the sum of the values of the parts: 10 kg at ₹26 plus 6 kg at ₹x must equal 16 kg at ₹35.

Write that one equation and the unknown rate falls out. No alligation diagram is needed.

Alligation is the same statement rearranged: the cheaper wheat sits 9 below the mean (35 − 26) and the dearer wheat 15 above it (50 − 35), so the quantities stand in the ratio 15 : 9 = 5 : 3 — which is 10 : 6.

Key facts

• Value is conserved: (quantity₁ × rate₁) + (quantity₂ × rate₂) = total quantity × mixture rate.
• Alligation gives the ratio of quantities as (dearer rate − mean) : (mean − cheaper rate).
• Here 10 kg : 6 kg reduces to 5 : 3, and so does (50 − 35) : (35 − 26) = 15 : 9, which confirms ₹50.

Common traps

• Dividing ₹300 by 16 instead of by 6 — the ₹300 belongs to the 6 kg alone
• Treating ₹35 as a selling price and hunting for a profit percentage
• Averaging 26 and 50 to get 38, which would only be right if the quantities were equal

No directly related past PYQ was found.