Question

A man bought goods worth rs 4500 and sold ⅓ of the goods at a loss of 10% At what gain per cent should he sell the remaining goods so as to gain 20% on the whole transaction?​

Answer 1

SOLUTION -

• CP of goods = ₹ 4500
• Gain = 20 %

SP of goods $= ( \frac{100 + gain\%}{100} ) \times cp$

$= ( \frac{100 + 20}{100} )\times 4500$

$= \frac{120}{100} \times 4500$

= ₹ 5400

CP of ⅓ of the goods

$= (\frac{1}{3} \times 4500)$

= ₹ 1500

☆ SP of ⅓ of the goods at a loss of 10 %

$= ( \frac{100 - loss\%}{100} ) \times cp$

$= ( \frac{100 - 10}{100} ) \times 1500$

$= \frac{90}{100} \times 1500$

= ₹ 1350

☆ SP of remaining goods =

= SP of all the goods - SP of ⅓ of the goods

= ₹ 5400 - ₹ 1350 = ₹ 4050

☆ CP of remaining goods =

= CP of all the goods - CP of ⅓ of the goods

= ₹ 4500 - ₹ 1500 = ₹ 3000

Gain = SP - CP

= ₹ 4050 - ₹ 3000 = ₹ 1050

Gain % = gain/CP × 100%

$= \frac{1050}{3000} \times 100\%$

= 35 %

hence, he should sell the remaining goods at a gain of 35 % .