At what rate percent on simple interest will a sum of money double itself in 30 years?
Answer: A
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Doubling means the interest equals the principal.
\[ P = \frac{P \times R \times 30}{100} \quad\Longrightarrow\quad 100 = 30R \]
\[ R = \frac{10}{3} = 3\tfrac{1}{3}\% \]
The principal cancels, so the answer holds for any sum.
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A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
Answer: D
\[ \text{SI} = \frac{P \times R \times T}{100} \]
\[ 840 = P\left(1 + \frac{3 \times 10}{100}\right) = 1.3P \]
\[ P = \frac{840}{1.3} = \text{Rs. } 646.15 \]
That value appears nowhere on the list, so the answer is none. The Rs. 525 offered would amount to only Rs. 682.50 over the same ten years.
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In what time a sum of money double itself at 3% per annum simple interest?
Answer: B
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Doubling means the interest equals the principal.
\[ P = \frac{P \times 3 \times T}{100} \quad\Longrightarrow\quad 100 = 3T \]
\[ T = \frac{100}{3} = 33\tfrac{1}{3} \text{ years} \]
The rule is simply \( T = \tfrac{100}{R} \) for doubling under simple interest.
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The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
Answer: C
Rs. 600 over ten years means Rs. 60 a year on the original principal.
First five years at the original principal:
\[ 5 \times 60 = \text{Rs. } 300 \]
Next five years with the principal trebled, so three times the yearly interest:
\[ 5 \times 180 = \text{Rs. } 900 \]
\[ \text{total} = 300 + 900 = \text{Rs. } 1200 \]
Trebling the whole Rs. 600 would give Rs. 1800; only the second half of the period is affected.
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Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
Answer: A
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Find the rate first.
\[ \text{SI} = 9200 - 8000 = 1200 \quad\Longrightarrow\quad 1200 = \frac{8000 \times R \times 3}{100} = 240R \]
\[ R = 5\% \]
At \( 5 + 2 = 7\% \):
\[ \text{SI} = \frac{8000 \times 7 \times 3}{100} = 1680 \quad\Longrightarrow\quad \text{amount} = \text{Rs. } 9680 \]
The extra 2% over three years adds \( 8000 \times 0.06 = 480 \) - the same answer directly.
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If x is the interest on y and y is the interest on z, the rate and time is the same on both the cases. What is the relation between x, y and z?
Answer: C
Write both statements with the same \( R \) and \( T \), and let \( k = \tfrac{RT}{100} \).
\[ x = yk, \qquad y = zk \]
Dividing one by the other:
\[ \frac{x}{y} = \frac{y}{z} \quad\Longrightarrow\quad y^{2} = xz \]
So \( y \) is the geometric mean of \( x \) and \( z \). Substituting directly gives the same thing: \( x = zk^{2} \) and \( y^{2} = z^{2}k^{2} = xz \).
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Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
Answer: D
Let \( p \) be the part at 5%; the rest, \( 2500 - p \), earns 6%.
\[ 0.05p + 0.06(2500 - p) = 140 \]
\[ 0.05p + 150 - 0.06p = 140 \quad\Longrightarrow\quad -0.01p = -10 \]
\[ p = \text{Rs. } 1000 \]
Checking: Rs. 50 from the 5% part and Rs. 90 from the Rs. 1500 at 6%.
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If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
Answer: D
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Growing from Re. 1 to Rs. 9 means interest of Rs. 8.
\[ 8 = \frac{1 \times R \times 20}{100} = 0.2R \]
\[ R = 40\% \]
The amount is 9 times the principal, so the interest is 8 times it - using 9 here would give 45%.
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4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
Answer: C
Let \( p \) be the part at 3%; the rest, \( 4000 - p \), earns 5%.
\[ 0.03p + 0.05(4000 - p) = 144 \]
\[ 0.03p + 200 - 0.05p = 144 \quad\Longrightarrow\quad -0.02p = -56 \]
\[ p = \text{Rs. } 2800 \]
Checking: Rs. 84 from the 3% part and Rs. 60 from the Rs. 1200 at 5%.
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If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Answer: D
\[ \text{SI} = \frac{P \times R \times T}{100} \]
"Produces rupees nine" means the interest itself is Rs. 9.
\[ 9 = \frac{1 \times R \times 40}{100} = 0.4R \]
\[ R = 22.5 = 22\tfrac{1}{2}\% \]
Here the 9 is the interest, not the amount - if it were the amount the interest would be 8 and the rate 20%, which is why that value is also on the list.
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