What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?
Answer: D
\[ \text{SI} = \frac{P \times R \times T}{100} \]
\[ \text{SI} = \frac{18000 \times 15 \times 4}{100} = \text{Rs. } 10{,}800 \]
\[ \text{amount} = 18000 + 10800 = \text{Rs. } 28{,}800 \]
The question asks what Kiran gets, so the principal is included; the interest alone is Rs. 10,800.
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In how many years, Rs. 200 will produce the same interest @ 5 % as Rs. 900 produce in 2 years @ 3 ½ %?
Answer: A
P = Rs 900, R = 3 ½ % = 7/2 %, T = 2 years.
Therefore,
S.I. = PRT/100
S.I. = Rs. (900 x 7/2 x 2/100) = Rs. 63
Now, P = Rs. 200, S.I. = Rs. 63, R = 5 %
Time = ((100 x 63) / (200 x 5) ) years = 6.3 years
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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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Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
Answer: D
Let \( p \) be the part at 6%; the rest, \( 1500 - p \), earns 5%.
\[ 0.06p + 0.05(1500 - p) = 85 \]
\[ 0.06p + 75 - 0.05p = 85 \quad\Longrightarrow\quad 0.01p = 10 \]
\[ p = \text{Rs. } 1000 \text{ at } 6\% \]
\[ \text{lent at } 5\% = 1500 - 1000 = \text{Rs. } 500 \]
The question asks for the 5% part, so the Rs. 1000 found first is not the answer.
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Find the simple interest on Rs. 78000 at 15(2/5) % per annum for 9 months.
Answer: D
\[ \text{SI} = \frac{P \times R \times T}{100} \]
The rate \( 15\tfrac{2}{5}\% \) is 15.4%, and nine months is \( \tfrac{3}{4} \) of a year.
\[ \text{SI} = \frac{78000 \times 15.4 \times 0.75}{100} \]
\[ = 780 \times 15.4 \times 0.75 = 780 \times 11.55 = \text{Rs. } 9009 \]
Leaving the period as 9 rather than \( \tfrac{9}{12} \) would inflate the answer twelvefold.
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In how many years will a sum of money doubles itself at 5% per annum on simple interest?
Answer: B
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Doubling means the interest equals the principal.
\[ P = \frac{P \times 5 \times T}{100} \quad\Longrightarrow\quad 100 = 5T \]
\[ T = 20 \text{ years} \]
The general rule for doubling under simple interest is \( T = \tfrac{100}{R} \).
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A certain sum is invested at simple interest at 18% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?
Answer: A
\[ \text{SI} = \frac{P \times R \times T}{100} \]
The two schemes share the sum and the two years, so only the 6% gap in rate matters.
\[ \frac{P \times (18 - 12) \times 2}{100} = 840 \]
\[ 0.12P = 840 \quad\Longrightarrow\quad P = \text{Rs. } 7000 \]
Checking: Rs. 2520 at 18% against Rs. 1680 at 12% - a difference of exactly Rs. 840.
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In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
Answer: A
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Work out the target interest first.
\[ \frac{5000 \times 4 \times 5}{100} = \text{Rs. } 1000 \]
Now find how long Rs. 4000 at 3% takes to earn the same:
\[ 1000 = \frac{4000 \times 3 \times T}{100} = 120\,T \]
\[ T = \frac{1000}{120} = 8\tfrac{1}{3} \text{ years} \]
The smaller principal at the lower rate needs longer, so the answer must exceed the 5 years - a quick sanity check.
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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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A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
Answer: A
Doubling means the interest equals the principal, so
\[ P = \frac{P \times R \times 10}{100} \quad\Longrightarrow\quad R = 10\% \]
Trebling needs interest of \( 2P \):
\[ 2P = \frac{P \times 10 \times T}{100} \quad\Longrightarrow\quad T = 20 \text{ years} \]
Under simple interest the interest accumulates linearly, so twice the interest takes exactly twice the time - under compound interest it would take less.
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