How much wheat (in kg, rounded off to the nearest integer) costing ₹36 per kg must be mixed with 55 kg of wheat costing ₹45 per kg so that there may be a gain of 20% by selling the mixture at ₹50 per kg?

Given:

Cost of wheat A = ₹36 per kg

Cost of wheat B = ₹45 per kg

Quantity of wheat B = 55 kg

Selling price of the mixture = ₹50 per kg

Desired profit = 20%

Calculation:

Let the quantity of wheat A to be mixed = x kg

Cost of the mixture = (Cost of wheat A × Quantity of A) + (Cost of wheat B × Quantity of B)

Total cost = 36x + 45 × 55

Total quantity = x + 55

Desired selling price = Cost price × (1 + Profit%)

50 × (x + 55) = (36x + 45 × 55) × (1 + 20 / 100)

50 × (x + 55) = 1.2 × (36x + 45 × 55)

50x + 50 × 55 = 1.2 × (36x + 45 × 55)

50x + 2750 = 1.2 × (36x + 2475)

50x + 2750 = 43.2x + 2970

50x − 43.2x = 2970 − 2750

6.8x = 220

x = 220 / 6.8 = 32.35 kg

∴ The quantity of wheat A required is approximately 32 kg (rounded to the nearest integer).