A shopkeeper mixes two types of rice costing ₹250/5 kg and ₹280/5 kg in the ratio 7 : 8. Find the net cost of the resultant mixture (per kg).

Correct — A. Put both prices on the same unit first, then take the weighted average.

₹250 per 5 kg = 250 ⁄ 5 = ₹50 per kg
₹280 per 5 kg = 280 ⁄ 5 = ₹56 per kg

Mixing 7 : 8, cost of 15 kg
= 7 × 50 + 8 × 56
= 350 + 448 = ₹798

Per kg = 798 ⁄ 15 = ₹53.20 → option (a).

Why the others are wrong

• (b)
  ₹32.50 — Option (b), ₹32.50, sits below ₹50, the cheaper of the two rices. A mixture can never cost less than its cheaper ingredient.
• (c)
  ₹52.30 — Option (c), ₹52.30, is inside the range but below the midpoint ₹53. The dearer rice carries the larger share (8 of 15 parts), so the answer must sit above ₹53.
• (d)
  ₹25.30 — Option (d), ₹25.30, is below both ₹50 and ₹56, so no mixture of the two reaches it. Like (b), it is the right digits in the wrong order.

A mixture's price is the weighted average of the ingredient prices, the weights being the quantities mixed.

Price = (q₁p₁ + q₂p₂) ⁄ (q₁ + q₂). A ratio can be used directly as the quantities, so 7 : 8 works as 7 kg and 8 kg.

Two checks bound the answer before any arithmetic. It must lie strictly between ₹50 and ₹56, and because the dearer rice has the greater weight it must lie above the midpoint ₹53.

All four options here are the digits 5, 3, 2 and 0 rearranged, so the bounding check is what separates them, not a glance.

Key facts

• ₹250 per 5 kg is ₹50 per kg, and ₹280 per 5 kg is ₹56 per kg.
• The weighted average is (7 × 50 + 8 × 56) ⁄ 15 = 798 ⁄ 15 = ₹53.20.
• A mixture price always lies strictly between the two ingredient prices.
• It lies nearer the price carrying the larger quantity, which is why ₹53.20 exceeds the midpoint ₹53.

Common traps

• Averaging ₹50 and ₹56 to ₹53 and ignoring the 7 : 8 weights
• Leaving the prices per 5 kg and reporting a figure five times too large

No directly related past PYQ was found.