Question

a shopkeeper has two varieties of rice A and B.By selling A at ₹75 per kg,he loses 20%;and by selling B at ₹90 per kg,he gains 25%.if he mixes A and B in the ratio 4:5 and sells the mixture at ₹110.25 per kg,then his profit percentage is​

Answer 1

Loss & profit problem

Given: The selling price of type A rice and type B rice are Rs. 75 and Rs. 90 at 20% loss and 25% gain respectively. Type A rice and type B rice are mixed in the ratio 4 : 5 and sold at Rs. 110.25 per kg.

To find: The profit percentage.

Solution:

Step 1. Finding the cost price of two types of rice:

• Cost price of type A rice is Rs. 75/(1 - 20/100) = Rs. 93.75
• Cost price of type B rice is Rs. 90/(1 + 25/100) = Rs. 72

Step 2. Finding the cost price of the mixture:

• Cost price of type A and type B rice are Rs. 93.75 and Rs. 72 respectively and they are mixed in the ratio 4 : 5.
• Thus the cost price of the mixture is
• = Rs. (93.75 × 4 + 72 × 5)/(4 + 5)
• = Rs. 245/3

Step 3. Finding the profit of selling the mixed rice:

• The mixed rice is sold at Rs. 110.25
• Then profit is Rs. (110.25 - 245/3)
• = Rs. 343/12

Step 4. Finding the profit percentage:

• Cost price = Rs. 245/3
• Profit = Rs. 343/12
• Therefore profit percentage is
• = Profit / Cost price × 100 %
• = 343/12 / 245/3 × 100 %
• = 35 %

Answer: Required profit percentage is 35%.