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

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Let CP be Rs x

case of loss,

SP of 1 orange = Rs 160/45

Loss = 20%

⇒SP = CP - Loss

= x - 20% of x = x - 0.2x = 0.8x

⇒160/45 = 0.8x

⇒x = Rs 40/9

case of gain,

Let the number of orange be y

SP of 1 orange = Rs 112/y

SP = CP + gain

= x + 20% of x = x +0.2x = 1.2x = 1.2×(40/9)

⇒112/y = 1.2×(40/9)

⇒y = 21

so, 21 oranges should she sell for rupees 112 to gain 20% on the whole.

case of loss,

SP of 1 orange = Rs 160/45

Loss = 20%

⇒SP = CP - Loss

= x - 20% of x = x - 0.2x = 0.8x

⇒160/45 = 0.8x

⇒x = Rs 40/9

case of gain,

Let the number of orange be y

SP of 1 orange = Rs 112/y

SP = CP + gain

= x + 20% of x = x +0.2x = 1.2x = 1.2×(40/9)

⇒112/y = 1.2×(40/9)

⇒y = 21

so, 21 oranges should she sell for rupees 112 to gain 20% on the whole.