Rakesh is a fruit vendor. To a customer he sells one kilogram of guavas at 20% loss and one kilogram mangoes at 40% profit, and he earns a profit of Rs.44. To another customer he sells one kilogram of mangoes and one kilogram of guavas each, at 20% profit and earns a profit of Rs.40. If he sells 3 kilograms of guavas and 5 kilograms of mangoes at 40% profit each, what is his overall profit?

Formula Used:

Profit = Selling Price - Cost Price

Profit Percentage = (Profit / Cost Price) × 100

Calculation:

Let the cost price of 1 kg of guavas be ₹g.

Let the cost price of 1 kg of mangoes be ₹m.

Scenario 1:

Sells 1 kg guavas at 20% loss. Selling price of guavas = g - 0.20g = 0.80g.

Sells 1 kg mangoes at 40% profit. Selling price of mangoes = m + 0.40m = 1.40m.

Total profit in Scenario 1 = (0.80g - g) + (1.40m - m) = -0.20g + 0.40m = 44 ------ (1)

Scenario 2:

Sells 1 kg guavas at 20% profit. Selling price of guavas = g + 0.20g = 1.20g.

Sells 1 kg mangoes at 20% profit. Selling price of mangoes = m + 0.20m = 1.20m.

Total profit in Scenario 2 = (1.20g - g) + (1.20m - m) = 0.20g + 0.20m = 40 ----- (2)

Add Equation 1 and Equation 2:

(-0.20g + 0.40m) + (0.20g + 0.20m) = 44 + 40

0.60m = 84

m = 84 / 0.60 = 840 / 6 = 140

The cost price of 1 kg of mangoes is ₹140.

Substitute the value of m in Equation 2:

0.20g + 0.20(140) = 40

0.20g + 28 = 40

0.20g = 40 - 28 = 12

g = 12 / 0.20 = 120 / 2 = 60

The cost price of 1 kg of guavas is ₹60.

Scenario 3:

Sells 3 kg of guavas at 40% profit.

Cost price of 3 kg guavas = 3 × 60 = ₹180.

Profit on 3 kg guavas = 40% of 180 = 0.40 × 180 = ₹72.

Sells 5 kg of mangoes at 40% profit.

Cost price of 5 kg mangoes = 5 × 140 = ₹700.

Profit on 5 kg mangoes = 40% of 700 = 0.40 × 700 = ₹280.

Overall profit = Profit on 3 kg guavas + Profit on 5 kg mangoes

Overall profit = 72 + 280 = ₹352.

His overall profit is ₹352.