A grocer mixes 40 kg of lentils costing ₹65 per kg with a certain quantity of lentils costing ₹80 per kg. If he sells the mixture at ₹75 per kg, making a 10% profit, what quantity of the second type of lentils did he mix?

Correct — B. A 10% profit means revenue = 1.1 × cost. Let x kg of the ₹80 lentils go in.

Cost = 40 × 65 + 80x = 2,600 + 80x
Revenue = 75 × (40 + x) = 3,000 + 75x

Set revenue = 1.1 × cost: 3,000 + 75x = 1.1 × (2,600 + 80x) = 2,860 + 88x
Collect terms: 140 = 13x
x = 140 ÷ 13 = 10.77 kg → option (b).

Why the others are wrong

• (a)
  25.98 kg — With 25.98 kg the cost is ₹4,678.40 for 65.98 kg, about ₹70.91 a kg. Selling at ₹75 then earns about 5.8%, not 10%.
• (c)
  35 kg — With 35 kg the cost is ₹5,400 for 75 kg, which is ₹72 a kg. Selling at ₹75 then earns 3 ÷ 72 ≈ 4.2%, not 10%.
• (d)
  40 kg — Equal quantities cost (65 + 80) ÷ 2 = ₹72.50 a kg, so ₹75 earns only about 3.4%. More of the ₹80 lentils push the cost up and the profit down.

The profit fixes the cost price of the mixture, not its selling price: CP = 75 ÷ 1.1 = 750⁄11 ≈ ₹68.18 a kg.

Alligation then gives the ratio directly. Cheaper : dearer = (80 − 68.18) : (68.18 − 65) = 130⁄11 : 35⁄11 = 26 : 7.

With 40 kg of the cheaper lentils, the dearer quantity is 40 × 7⁄26 ≈ 10.77 kg.

Key facts

• Mixture CP = SP ÷ (1 + profit%) = ₹75 ÷ 1.1 ≈ ₹68.18 a kg.
• Alligation: cheaper : dearer = (dearer price − mixture CP) : (mixture CP − cheaper price).
• Here the ratio is 26 : 7, so 40 kg of the ₹65 lentils pairs with 280⁄26 ≈ 10.77 kg of the ₹80 lentils.

Common traps

• Using ₹75 as the mixture's cost: alligation then gives 5 : 10 and an answer of 80 kg, which is not offered.
• Taking 10% off ₹75 (₹67.50) instead of dividing by 1.1, which gives a ratio of 5 : 1 and 8 kg.
• Setting the alligation ratio the wrong way round, which puts 40 × 26⁄7 ≈ 148.6 kg of the dearer lentils in.

No directly related past PYQ was found.