Question

Q9. A shopkeeper mixed some quantity of another type of rice with a price of Rs. 15 per kg to 10 kg of rice at the rate of Rs. 10 per kg and the mixture at the rate of Rs. 14 per kg.​

Answer 1

Answer:

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Let quantity of second variety of rice = x kg

Total Cost Price =∑(Amount×Price rate)

=10×10+x×15

=15x+100 Rs

Total Selling Price of mixture = Total amount of mixture × rate of mixture

=(10+x)×14=140+14x Rs

Gain percentage = 5%

∴Gain=5% of Cost Price=

100

5

×(15x+100)=

4

3x

+5

We know that, Gain=Selling price−Cost price

⇒

4

3x

+5=(140+14x)−(15x+100)

⇒

4

3x

+5=140+14x−15x−100

⇒

4

3x

=35−x

⇒

4

7x

=35

∴x=

7

35×4

=20

Hence, quantity of second variety of rice = x kg = 20 kg.

Answer 2

Let quantity of second variety of rice = x kg

Total Cost Price =∑(Amount×Price rate)

=10×10+x×15

=15x+100 Rs

Total Selling Price of mixture = Total amount of mixture × rate of mixture

=(10+x)×14=140+14x Rs

Gain percentage = 5%

∴Gain=5% of Cost Price=

100

5

×(15x+100)=

4

3x

+5

We know that, Gain=Selling price−Cost price

⇒

4

3x

+5=(140+14x)−(15x+100)

⇒

4

3x

+5=140+14x−15x−100

⇒

4

3x

=35−x

⇒

4

7x

=35

∴x=

7

35×4

=20

Hence, quantity of second variety of rice = x kg = 20 kg