5 Marks Questions

Question 15 Marks

Romesh borrowed $Rs. 2000 $ at $2\%$ per annum and $Rs. 1000$ at $5\%$ per annum. He cleared his debt after $2$ years by giving $Rs. 2800$ and a watch. What is the cost of the watch?

Answer

Principal amount borrowed by Romesh $(P) = Rs. 2000$
Time period $(T) = 2$
years Rate of interest $(R) = 2\%$ p.a.
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{2000\ \times\ 2\ \times\ 2}{100}$
$=\text{Rs. }80$ Principal amount borrowed by Romesh $(P) = Rs. 1000$
Time period $(T) = 2$
years Rate of interest $(R) = 5%$ p.a.
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{1000\ \times\ 5\ \times\ 2}{100}$
$=\text{Rs. }100$
Total amount that he will have to return $= Rs. 2000 + Rs. 1000 + Rs. 80 + Rs. 100 = Rs. 3180$
Amount repaid $= Rs. 2800$
Value of the watch $= Rs. 3180 - Rs. 2800 = Rs. 380$

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Question 25 Marks

Mr. Garg lent $Rs. 15000$ to his friend. He charged $15\%$ per annum on $Rs. 12500$ and $18\%$ on the rest. How much interest does he earn in $3$ years?

Answer

Principal amount $(P) = Rs. 12500$
Time period $(T) = 3$ years Rate of interest $(R) = 15\%$ p.a.
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{12500\ \times\ 15\ \times\ 3}{100}$
$=\text{Rs. }5625$ Rest of the amount lent $= Rs. 15000 - Rs. 12500 = Rs. 2500$
Rate of interest $= 18 \%$ p.a.
Time period $= 3$ years
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{2500\ \times\ 18\ \times\ 3}{100}$
$=\text{Rs. }1350$ Total interest earned $= Rs. 5625 + Rs. 1350 = Rs. 6975$

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Question 35 Marks

Rohit borowed $Rs. 600000$ from a bank at $9\%$ per annum for $2$ years. He lent this sum of money to Rohan at $10\%$ per annum for $2$ years. How much did Rohit earn from this transaction?

Answer

Principal amount lent out by Rohit $(P) = Rs. 60000$
Time period $(T) = 2$
years Rate of interest $(R) = 10\%$ p.a.
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{60000\ \times\ 10\ \times\ 2}{100}$
$=\text{Rs. }12000$
Principal amount borrowed by Rohit from the bank $(P) = Rs. 60000$
Time period $(T) = 2$ years
Rate of interest $(R) = 9\%$ p.a.
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{60000\ \times\ 9\ \times\ 2}{100}$
$=\text{Rs. }10800$
Amount gained by Rohit $= Rs. 12000 - Rs. 10800 = Rs. 1200$

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Question 45 Marks

Shikha deposited $Rs. 2000$ in a bank which pays $6\%$ simple interest. She withdrew $Rs. 700$ at the end of first year. What will be her balance after $3$ years?

Answer

$\text { Principal amount deposited }(P)=\text { Rs } 2000$
$\text { Time period }(T)=1 \text { year }$
$\text { Rate of interest }(R)=6 \% \text { p.a. }$
$\text { Simple interest }=\frac{P \times R \times T}{100}$
$=\frac{2000 \times 6 \times 1}{100}$
$=\text { Rs. } 120$
$\text { So amount after } 1 \text { year }=\text { Principal amount }+ \text { Interest }=2000+120=\text { Rs. } 2120$
$\text { After } 1 \text { year, amount withdrawn }=\text { Rs. } 700$
$\text { Principal amount left }\left(P_1\right)=\text { Rs. } 2120-\text { Rs.. } 700=\text { Rs. } 1420$
$\text { Time period }(T)=2 \text { years }$
$\text { Rate of interest }(R)=6 \% \text { p.a. }$
$\text { Interest after } 2 \text { years }=\frac{P \times R \times T}{100}$
$=\frac{1420 \times 6 \times 2}{100}$
$=\text { Rs. } 170.40$
$\text { Total amount after } 3 \text { years = Rs. } 1420+\text { Rs. } 170.40=\text { Rs. } 1590.40$

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Question 55 Marks

Rakesh lent out $Rs. 8000$ for $5$ years at $15\%$ per annum and borrowed $Rs. 6000$ for $3$ years at $12\%$ per annum. How much did he gain or lose?

Answer

Principal amount lent out by Rakesh $(P) = Rs. 8000$
Time period $(T) = 5$ year
Rate of interest $(R) = 15\%$ p.a.
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{8000\ \times\ 15\ \times\ 5}{100}$
$=\text{Rs. }6000$
Principal amount borrowed by Rakesh $(P) = Rs. 6000$
Time period $(T) = 3$ year
Rate of interest $(R) = 12\%$ p.a.
Simple interest $=\frac{\text{P}\ \times\ \text{R}\ \times\ \text{T}}{100}$
$=\frac{6000\ \times\ 12\ \times\ 3}{100}$
$=\text{Rs. }2160$
Amount gained by Rakesh $= Rs. 6000 - Rs. 2160 = Rs. 3840$

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