A grocer brought a number of fruit baskets for Rs800 Five baskets were lost in transe He sold - Maths - Quadratic Equations

Question

A grocer brought a number of fruit baskets for Rs800 Five
baskets were lost in transe He sold the rst for Rs 8 per basket
more thanwhat he paid for them and made a profit of Rs180 on his
outlay
Find the number of baskets bought by him

Lalit Mehra · Accepted Answer

Let the number of baskets bought by grocer be x.

Given, cost price of x baskets = Rs 800

∴ Cost price of each basket $= Rs \frac{800}{x}$

When five baskets were lost, then selling price of each remaining basket $= Rs (\frac{800}{x} + 8)$

$∴ Selling price of (x - 5) baskets = Rs (\frac{800}{x} + 8) (x - 5)$

Profit made by the grocer = Rs 180 (Given)

$∴ (\frac{800}{x} + 8) (x - 5) - 800 = 180 [\Pr o f i t = S P - C P] \Rightarrow 8 (\frac{100 + x}{x}) (x - 5) = 800 + 180 = 980$

⇒ 2 (100 + x) (x – 5) = 245 x

⇒ 2x² + 190x – 1000 = 245 x

⇒ 2x² – 55x – 1000 = 0

⇒ 2x² – 80x + 25x – 1000 = 0

⇒ 2x(x – 40) + 25 (x – 40) = 0

⇒ (2x + 25) (x – 40) = 0

⇒ 2x + 25 = 0 or x – 40 = 0

$\Rightarrow x = - \frac{25}{2} or x = 40$

∴ x = 40 (Number of baskets cannot be negative)

Thus, the number of baskets bought by the grocer is 40.

3

A grocer brought a number of fruit baskets for Rs800. Five baskets were lost in transe. He sold the rst for Rs 8 per basket more thanwhat he paid for them and made a profit of Rs180 on his outlay. Find the number of baskets bought by him.

A grocer brought a number of fruit baskets for Rs800. Five baskets were lost in transe. He sold the rst for Rs 8 per basket more thanwhat he paid for them and made a profit of Rs180 on his outlay.

Find the number of baskets bought by him.