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Maths 2 Mark Question

Compound Interest · Maharashtra Board STD 8 (MSBSHSE - English Medium). 6 questions.

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2 Mark Question

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6 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
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 $=\text{P}\Big(1-\frac{\text{R}}{100}\Big)^{\text{-n}}$
$\Rightarrow9,680\Big(1-\frac{12}{100}\Big)^{-2}$
$=9,680(0.88)^{-2}$
$=12,500$
Thus, the purchase price of the refrigerator was Rs. 12,500.
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Question 22 Marks
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 $=\text{P}\Big(1-\frac{\text{R}}{100}\Big)^{\text{-n}}$
$\Rightarrow43,740\Big(1-\frac{10}{100}\Big)^{-3}$
$=43,740(0.90)^{-3}$
$=60,000$
Thus, the purchase price of the machine was Rs. 60,000.
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Question 32 Marks
The population of a certain city was 72000 on the last day of the year 1998. During next year it increased by 7% but due to an epidemic it decreased by 10% in the following year. What was its population at the end of the year 2000?
Answer
Population at the end of the year 2000 $=\text{P}\Big(1+\frac{\text{R}_{1}}{100}\Big)\Big(1-\frac{\text{R}_{2}}{100}\Big)$
$=72,000\Big(1+\frac{7}{100}\Big)\Big(1-\frac{10}{100}\Big)$
$=72,000(1.07)(0.9)$
$=69,336$
Thus, the population at the end of the year 2000 was 69,336.
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Question 42 Marks
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 $=\text{P}\Big(1-\frac{\text{R}_{1}}{100}\Big)\Big(1+\frac{\text{R}_{2}}{100}\Big)\Big(1+\frac{\text{R}_{3}}{100}\Big)$
$\Rightarrow500,000\Big(1-\frac{4}{100}\Big)\Big(1+\frac{5}{100}\Big)\Big(1+\frac{10}{100}\Big)$
$=500,000(0.96)(1.05)(1.10)$
$=554,400$
Thus, the net profit is Rs. 554,400.
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Question 52 Marks
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 $=\text{P}\Big(1-\frac{\text{R}}{100}\Big)^{\text{n}}$
$\Rightarrow30,000\Big(1-\frac{25}{100}\Big)^{3}$
$=30,000(0.75)^{3}$
$=12,656.25$
Thus, the value of the house after three years will be Rs. 12,656.25.
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Question 62 Marks
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 $=\text{P}\Big(1+\frac{\text{R}}{100}\Big)\Big(1-\frac{\text{R}}{100}\Big)$
$\Rightarrow17,000\Big(1+\frac{5}{100}\Big)\Big(1-\frac{4}{100}\Big)$
$=17,000(1.05)(0.96)$
$=17,136$
Thus, the cost the TV in 2001 was Rs. 17,136.
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