Chapter 14 - Compound Interest (Part - 5), Class 8, Maths RD Sharma Solutions | RD Sharma Solutions for Class 8 Mathematics PDF Download

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Question 1:

Ms. Cherian purchased a boat for Rs 16000. If the total cost of the boat is depreciating at the rate of 5% per annum, calculate its value after 2 years.

ANSWER:

Value of the boat after two years = P(1 − R/100)ⁿ

⇒ 16,000(1 − 5/100)²

= 16,000(0.95)²

= 14,440

Thus, the value of the boat after two years will be Rs 14,440.

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Question 2:

The value of a machine depreciates at the rate of 10% per annum. What will be its value 2 years hence, if the present value is Rs 100000 ? Also, find the total depreciation during this period.

ANSWER:

Value of the machine after two years = P(1 − R/100)ⁿ

⇒ 100,000(1 − 10/100)²

= 100,000(0.90)² = 81,000

Thus, the value of the machine after two years will be Rs 81,000.

Depreciation = Rs 100,000 − Rs 81,000                       

= Rs 19,000

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Question 3:

Pritam bought a plot of land for Rs 640000. Its value is increasing by 5% of its previous value after every six months. What will be the value of the plot after 2 years?

ANSWER:

Given: P =  Rs 64,000

R =  5% for every six monthsValue of the plot after two years  =  P(1 + R/100)ⁿ

⇒ 64,000(1 + 5/200)⁴ 

= 64,000(1.025)⁴ 

= 706,440.25

Thus, the value of the plot after two years will be Rs 706,440.25.

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Question 4:

Mohan purchased a house for Rs 30000 and its value is depreciating at the rate of 25% per year. Find the value of the house after 3 years.

ANSWER:

Value of the house after three years = P(1 − R/100)ⁿ

⇒ 30,000(1 − 25/100)³

= 30,000(0.75)³

= 12,656.25

Thus, the value of the house after three years will be Rs 12,656.25. 

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Question 5:

The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago. If its present value is Rs 43740, find its purchase price.

ANSWER:

Purchase price = P(1 − R/100) ^{− n}

⇒ 43,740(1 − 10/100) ^{− 3} 

= 43,740(0.90) ^{− 3}

= 60,000

Thus, the purchase price of the machine was Rs 60,000.

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Question 6:

The value of a refrigerator which was purchased 2 years ago, depreciates at 12% per annum. If its present value is Rs 9680, for how much was it purchased?

ANSWER:

Purchase price = P(1 − R/100)^{− n}

⇒ 9,680(1 − 12/100)^{− 2} 

= 9,680(0.88)⁻² 

= 12,500

Thus, the purchase price of the refrigerator was Rs 12,500.

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Question 7:

The cost of a T.V. set was quoted Rs 17000 at the beginning of 1999. In the beginning of 2000 the price was hiked by 5%. Because of decrease in demand the cost was reduced by 4% in the beginning of 2001. What was the cost of the T.V. set in 2001?

ANSWER:

Cost of the TV = P(1 + R/100)(1 − R/100)

⇒ 17,000(1 + 5/100)(1 − 4/100)

= 17,000(1.05)(0.96)

= 17,136

Thus, the cost the TV in 2001 was Rs 17,136.

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Question 8:

Ashish started the business with an initial investment of Rs 500000. In the first year he incurred a loss of 4%. However during the second year he earned a profit of 5% which in third year rose to 10%. Calculate the net profit for the entire period of 3 years.

ANSWER:

Profit for three years = P(1 − R₁/100)(1 + R₂/100)(1 + R₃/100)

⇒ 500,000(1 − 4/100)(1 + 5/100)(1 + 10/100)

= 500,000(0.96)(1.05)(1.10)

= 554,400

Thus, the net profit is Rs 554,400.