5 Marks Questions

Question 15 Marks

If ₹250 is to be divided amongst Ravi, Raju and Roy, so that Ravi gets two parts, Raju three parts and Roy five parts. How much money will each get? What will it be in percentages?

Answer

The parts which the three boys are getting can be written in terms of ratios as $2 : 3 : 5.$
Total of the parts $= 2 + 3 + 5 = 10.$
Amounts received by each
$\frac{2}{10} \times₹250 = ₹50$
$\frac{3}{10} \times₹250 = ₹75$
$\frac{5}{10}\times ₹250 = ₹125$
Therefore, Percentages of money for each
Ravi gets $\frac{2}{10} \times 100% = 20%$
and, Raju gets $\frac{3}{10} \times 100% = 30%$
Also, Roy gets $\frac{5}{10} \times 100% = 50%$

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Question 25 Marks

Anita takes a loan of $₹5,000$ at $15\%$ per year as rate of interest. Find the interest she has to pay at the end of one year.

Answer

The sum borrowed $= ₹ 5,000$, Rate of interest $= 15\%$ per year.
This means if $₹100$ is borrowed, she has to pay $₹15$ as interest for one year. If she has borrowed $₹5000$, then the interest she has to pay for one year
$= ₹\frac{15}{100} \times 5000=₹750$
So, at the end of the year she has to give an amount of $₹5,000 + ₹750 = ₹5,750$
We can write a general relation to find interest for one year. Take $P$ as the principal or sum and $R \%$ as Rate per cent per
annum.
Now on every $₹ 100$ borrowed, the interest paid is $₹ R$
Therefore, on $₹P$ borrowed, the interest paid for one year would be $\frac{R \times P}{100}=\frac{P \times R}{100}$

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Question 35 Marks

Selling price of a toy car is $₹ 540$. If the profit made by shopkeeper is $20\%$, what is the cost price of this toy?

Answer

We are given that $SP = ₹ 540$ and the Profit $= 20\%.$
We need to find the $CP.$
Profit $= 20\%$ of $CP$ and $SP = CP +$ Profit
So, $540 = CP + 20\%$ of $CP$
$CP + \frac{20}{100} \times \mathrm{CP}=\left[1+\frac{1}{5}\right] \mathrm{CP}$
$=\frac{6}{5} \mathrm{CP}$
Therefore, $540 \times \frac{5}{6}=\mathrm{CP}$ or $₹ 450 = CP$
Thus, the cost price is $₹450.$

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