by selling 45 oranges for rs. 160, a woman loses 20%. how many oranges should ahe sell for rs. 112 to gain 20% on the whole?
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Let CP be ₹ x
case of loss,
SP of 1 orange = ₹ 160 ÷ 45
Loss = 20%
⇒SP = CP - Loss
= x - 20% of x
= x - 0.2x = 0.8x
⇒160÷45 = 0.8x
⇒x = ₹40/9
case of gain,
Let the number of orange be y
SP of 1 orange = ₹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.
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