Question

A shopkeeper has 300 kg rice. He sold some part of it at 10% profit and remainder at 20% profit. On the whole he earned 18% profit, how much quantity did he sell at 20% profit?
1. 240 kg
2. 60 kg
3. 200 kg
4. 180 kg

Answer 1

Correct Answer - Option 1 : 240 kg

Given:

Total quantity of rice = 300 kg

Profit percent on 1^st part = 10%

Profit percent on 2^nd part = 20%

Profit percent on the whole = 18%

Formula used:

S.P = [(100 + Profit%)/100] × C.P

Concept used:

Profit and loss is always calculated on C.P

Calculation:

Let total C.P of 300 kg rice be Rs. 300

C.P of 1 kg of rice = Rs. 1

Again, let X kg of rice sold at 10% profit

Quantity of rice sold at 20% profit = 300 – X

C.P of X kg of rice = X 

C.P of (300 – X) kg of rice = (300 – X)

The profit percent on X kg = 10%

S.P = [(100 + Profit%)/100] × C.P

⇒ [(100 + 10)/100] × X

⇒ 11X / 10

Similarly, profit percent on (300 – X) kg = 20%

S.P = [(100 + Profit%)/100] × C.P

⇒ [(100 + 20)/100] × (300 – X)

⇒ [120/100] × (300 – X)

⇒ 6(300 – X)/5

Now, profit earned on 300 kg = 18%

S.P = [(100 + Profit%)/100] × C.P

⇒ [(100 + 18)/100] × 300

⇒ 118/100 × 300

⇒ 354

Total S.P = 11X/10 + 6(300 – X)/5 = 354

⇒ 11X/10 + 6(300 – X)/5 = 354

⇒ (11X + 3600 – 12X) = 3540

⇒ X = 3600 – 3540

⇒ 60

The quantity sold at 20% profit = 300 – 60 = 240 kg

∴ The quantity sold at 20% profit is 240 kg.