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.
Please log in or register to report this question.
A TV can be bought for Rs. 20000 cash or by paying in four equal monthly installments with an initial down payment of Rs. 4000. If the rate of interest for this facility is 8% per annum, then what would be the installment charged for each month?
Answer: D
After the down payment the balance is \( 20000 - 4000 = \text{Rs. } 16{,}000 \), cleared by four monthly installments of \( x \).
Carry everything forward to the end of month 4. The debt grows for 4 months, while the installments earn interest for 3, 2, 1 and 0 months:
\[ 16000\left(1 + \frac{8}{100} \times \frac{4}{12}\right) = x\left[\left(1 + \tfrac{8}{100}\cdot\tfrac{3}{12}\right) + \left(1 + \tfrac{8}{100}\cdot\tfrac{2}{12}\right) + \left(1 + \tfrac{8}{100}\cdot\tfrac{1}{12}\right) + 1\right] \]
\[ 16000 \times 1.026667 = x(1.02 + 1.013333 + 1.006667 + 1) \]
\[ 16426.67 = 4.04\,x \quad\Longrightarrow\quad x = \text{Rs. } 4066.01 \]
Dividing the balance by four gives Rs. 4000, which ignores the interest entirely - hence that distractor.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
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 \( T = \tfrac{100}{R} \).
Please log in or register to report this question.
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.
Please log in or register to report this question.
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.
Please log in or register to report this question.
