Question

By selling 45 oranges for 160 rupees, a woman loses 20%. How many oranges should she sell for 112 rupees to gain 20% on the whole?

Answer 1

Dear Student,
Let CP be Rs x
case of loss,
SP of 1 orange = Rs $\frac{160}{45}$
Loss = 20%
⇒SP = CP - Loss
= x - 20% of x = x - 0.2x = 0.8x
⇒ $\frac{160}{45}$ = 0.8x
⇒x = Rs $\frac{40}{9}$
case of gain,
Let the number of orange be y
SP of 1 orange = Rs $\frac{112}{y}$
SP = CP + gain
= x + 20% of x = x +0.2x = 1.2x = 1.2×(40/9)
⇒$\frac{112}{y}$ = 1.2×($\frac{40}{9}$)
⇒y = 21
so, 21 oranges should she sell for rupees 112 to gain 20% on the whole.

Regards