2 Marks Questions

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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