Question

A fruit-seller bought x apples for ₹ 1200.

1. Write the cost price of each apple in terms of x. 
2. If 10 of the apples were rotten and he sold each of the rest at ₹ 3 more than the cost price of each, write the selling price of (x – 10) apples. 
3. If he made a profit of ₹ 60 in this transaction, form an equation in x and solve it to evaluate x.

Answer 1

i. Cost price of each apple $$= ₹\ \frac{1200}{x}$$. 

ii. Selling price of each good apple $$= ₹\ \left(\frac{1200}{x} + 3\right)$$. 

Selling price of $$(x - 10)$$ apples $$= (x - 10)\left(\frac{1200}{x} + 3\right)$$. 

iii. Profit $$= \text{Total SP} - \text{Total CP} = 60$$:

$$(x - 10)\left(\frac{1200}{x} + 3\right) - 1200 = 60$$ 

$$(x - 10)\left(\frac{1200 + 3x}{x}\right) = 1260$$ 

Dividing by 3: $$(x - 10)\left(\frac{400 + x}{x}\right) = 420$$

$$(x - 10)(x + 400) = 420x$$

$$x^2 + 390x - 4000 = 420x$$

$$x^2 - 30x - 4000 = 0$$

Factoring: $$(x - 80)(x + 50) = 0$$

$$x = 80 \quad \text{or} \quad x = -50$$ 

Since the number of apples cannot be negative, $$x = 80$$.