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Simple Interest Questions

1. Shubhranshu deposited Rs 8000 at simple interest which amounted to Rs 9200 after 3 years . Had the interest been 2% more, how much amount she would have got?




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Correct Ans:Rs 9680
Explanation:
----> Amount = simple interest + principal

----> 9200 = simple interest + 8000

----> simple interest = 9200 – 8000
----> = Rs 1200
----> if r % be the rate of interest ,
----> Then from, simple interest = ((principal * rate% * time)/100)
----> 1200 = ((8000 * r * 3)/100)
----> r = 5%
----> 2% more interest that is 7% interest
----> simple interest = ((8000 * 7 * 3)/100)
----> = Rs 1680
----> thus amount he will get is Rs 8000 + Rs 1680 = Rs 9680

Hence, option B is correct.
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2. The SI on certain sum of money for 23 months at the rate of 7% per annum exceeds the SI on the same sum at 7% per annum for 19 months by Rs. 672. Then find the sum




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Correct Ans:Rs. 28800
Explanation:
Let the sum be P.
---> Then, ((P * 7 * 23)/12 * 100) - ((P * 7 * 19)/ 12 * 100 ) = 672
---> or, 161P – 133P = 672 * 100 * 12
---> P = ((672 * 100 * 12)/28) = Rs. 28800

Hence, option (B) is correct.
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3. Virat has Rs. 9000. He gives this money to Mahendra on simple interest and after 4 years received the double amount. If the interest rate is 5% more than the previous, in how many years this amount will be doubled?




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Correct Ans:3(1/3)years
Explanation:
---> S.I. = (P * r * t/100)
---> 9000 = (9000 * r * 4/100)
---> r = 25%
---> New rate = 25 + 5 = 30%
---> 9000 = 9000 * 30% * t
---> t = 3(1/3)years
--->Hence, option D is correct.
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4. A sum of Rs 1750 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. The interest on each part is(in Rs)




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Correct Ans:60
Explanation:
Let first part = Rs x
Second part = Rs (1750 – x)
According to the question,

-----> x * (8/100) = (1750 - x) * (6/100)
-----> 8x+6x = 1750 * 6
-----> 14x = 1750 *6
-----> x = ((1750 * 6)/14)
-----> x = 750

----> Interest = 8% of Rs 750
------> (8/100)*750
------> Rs 60

Hence the answer is : 60
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5. On a certain Principal if the Simple interest for two years is Rs 2400 and Compound interest for the two years is Rs 2544, what is the rate of Interest?




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Correct Ans:12 percent
Explanation:
According to the question:
Simple interest for two years is = Rs 2400
Compound interest for the two years is = Rs 2544
Difference between SI and CI will be = 144
Since it is for 2 years, rate of interest will be = √144 (difference b/w CI and SI) = 12%
Hence the answer is : 12 %
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6. An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes 




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Correct Ans:10.25%
Explanation:
Let the sum be Rs. 100.
WKT, SI = PNR/100
SI for first 6 months = (100 x 1 x 10)/(100 x 2) = Rs. 5
New principal = 100 + 5 = Rs. 105

SI fo last 6 months = (105 x 1 x 10)/(100 x 2) = Rs. 5.25
Therefore, amount at the end of 1 yr = 100 + 5 + 5.25
= Rs. 110.25
Effective rate = 110.25 - 100 = 10.25%.
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7. Ravi borrowed some money at the rate of 4% per annum for the first 3 yr, at the rate of 8% per annum for the next 2 yr and at the rate of 9% per annum for the period beyond 5 yr. If he pays a total simple interest of Rs. 19,550 at the end of 7 yr, how much money did he borrow? 




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Correct Ans:Rs. 42,500
Explanation:
Let the Ravi borrowed amount be 'X'.
WKT, SI = PNR/100
19550 = [(X x 4 x 3)/100] + [(X x 8 x 2)/100] + [(X x 9 x 2)/100]
19550 = [12X + 16X + 18X]/100
19550 = 46X/100
X = (19550 x 100)/46
X = Rs. 42,500
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8. Mr. Phanse invests an amount of Rs. 24,200 at the rate of 4% per annum for 6 yr to obtain a simple interest. Later he invests the principal amount as well as the amount obtained as simple interest for another 4 yr at the same rate of interest. What amount of simple interest will he obtain at the end of the last 4 yr? 




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Correct Ans:Rs. 4801.28
Explanation:
Given: Principal - Rs. 24,200; R - 4%; N - 6yr
WKT, SI = PNR/100
SI = (24200 x 6 x 4)/100
= Rs. 5808

He invests the principal amount as well as the amount obtained as simple interest for another 4 yr at the same interest.
Therefore, new pricipal = 24200 + 5808 = Rs. 30008
SI = (30008 x 4 x 4)/100
SI = Rs. 4801.28
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9. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both as interest. The rate of interest per annum is 




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Correct Ans:10%
Explanation:
WKT, SI = PNR/100
A lent Rs. 5000 to B for 2 years,
= [(5000 x r x 2)/100]

A lent Rs. 3000 to C for 4 years,
= [(3000 x r x 4)/100]

As per the question,
[(5000 x r x 2)/100] + [(3000 x r x 4)/100] = 2200
[100 x r] + [120 x r] = 2200
r x 220 = 2200
r = 10%
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10. If the annual rate of simple interest increases from 10% to 12(1/2)%, a man's yearly increases by Rs. 1250. His principal (in rupees) is ? 




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Correct Ans:50,000
Explanation:
(12(1/2)% - 10%) x = 1250
(25/2% - 10%) x = 1250
5/200 x = 1250
1/40 x = 1250
x = 50,000
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11. What will the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years.




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Correct Ans:2 : 3
Explanation:
We know that,
SI = Pnr/100
Let the principal be P and rate of interest be R
SI = [P*6*R/100] / [P*9*R/100]
SI = 6/9 = 2/3
SI = 2 : 3
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12. The simple interest on a certain sum for 8 months at 4% per annum is Rs. 129 less than the simple interest on the same sum for 15 months at 5% per annum. The sum is:




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Correct Ans:Rs. 3600
Explanation:
SI = Pnr/100
Let the sum be Rs. P
(P*5*15) / (100*12) - (P*4*8) / (100*12) = 129
[P / (100*12)] (75 - 32) = 129
P*43 / (100*12) = 129
P = 129*1200 / 43
P = 3*1200 = 3600
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13. The rates of simple interest in two banks x and y are in the ratio of 10 : 8. Rajini wants to deposit her total savings in two banks in such a way that she receives equal half-yearly interest from both. She should deposit the savings in banks x and y in the ratio of: 




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Correct Ans:4:5
Explanation:
Let the savings be P and Q and rates of Sl be 10x and 8x, respectively
Then, P* 10x * 1/2 * 1/100 = Q * 8x * 1/2 * 1/100
10P = 80
P/Q = 8/10 = 4/5
P:Q = 4:5
Hence, option A is correct.
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14. A sum of Rs.725 is lent in the beginning of the year at a certain rate of interest. After 8 months, a sum of Rs.362.50 more is lent but at a rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest? 




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Correct Ans:3.46%
Explanation:
Assume,
Original rate is for 1 year and the new rate is for only 4 months i.e. 1/3 year(s).
Let the original rate be R%
Then, new rate = (2R)%
Formula to calculate Simple Interest:
SI = PRT/100
SI= Simple Interest; P=Principal
r=Interest rate; t=time
Now,
⸫[(725 x R x 1)/(100)]+[(362.50 x 2R x 1)/(100 x 3)]= 33.50
Taking LCM, we get 300
(2175 + 725) R = 33.50 x 300
(2175 + 725) R = 10050
(2900)R = 10050
R = 10050/2900 = 3.46
Original rate = 3.46%
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15. A person lent some amount to his friend at 20% S.I. After 2 years, Rs 5000 was repaid and the rest amount was repaid 25% P.A. If 3rd year's interest is 6/11 of first 2 years intrest. Find the amount of money that was let out initially?




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Correct Ans:Rs 39285
Explanation:
Let sum = P
For 2 years
r = 20%
we know that,
SI = Pnr/100
SI = (P*2*20)/100
= 2P/5
Amount after 2nd year = P + 2P/5

For 3rd year
given that, SI = 6/11 of first 2yrs SI, P = P - 5000, n = 1, r = 25%.
SI = Pnr/100
6/11(2P/5) = (P - 5000)*1*25/100
12P/55 = (P - 5000)/4
48P = 55P - 275000
55P - 48P = 275000
7P = 275000
P = 275000/7
P = Rs 39285.71 (approx.)
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16. According to the new plan rolled out by Axis bank, the rate of simple interest on a sum of money is x% per annum for the first 4 years, y% per annum for the next 8 years and 10% per annum for the beyond the first 12 years. Ram invests some amount of money then the simple interest received by Ram at the end of 25 years is Rs. 29800. Other person, Mohan"™s investments sum is same as the Ram"™s investments then the simple interest revived by Mohan at the end of 32 years is Rs. 36,800. If Ram invests only for 3 years then the total SI received by his is Rs. 3,600 and Mohan invest only for 5 years then the total SI received by him is Rs. 6,300. If Ram had invested the same amount of money only for 15 years then how much simple interest he would have received?




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Correct Ans:None of these
Explanation:
Let the investments of Ram and Mohan = Rs. P
According to the question,
The simple interest received by Ram at the end of 25 years is Rs. 29800
SI = Pnr/100
10% for remaining 13 years in 25 years.
29800 = p × 4 × x% + p × 8 × y% + p × 13 × 10% ----- (i)

The simple interest revived by Mohan at the end of 32 years is Rs. 91000
10% for remaining 20 years in 32 years.
36800 = p × 4 × x% + p × 8 × y% + p × 20 × 10% ----- (ii)

Equation (ii) – equation (i)
(p*20*10)/100 - (p*13*10)/100 = 7000
(20p - 13p)/10 = 7000
7p/10 = 7000
P = 10,000

Now, when Ram invest only for 3 years then
10,000 × 3 × x% = 3600
3x = 36
x = 12% per annum

If Mohan invests only for 5 years then the total SI received by him
10,000 × 4 × x% + 10000 × 1 × y% = 6300
10000 × 4 × 12% + 10000 × y% = 6300
10,000[(4*12)/100 + y/100] = 6300
100[(4*12)/100 + y/100] = 63
100/100 [48 + y] = 63
48 + y = 63
y = 15% per annum

The simple interest he would have received = 10,000 × 4 × 12% + 10000 × 8 × 15% + 10000 × 3 × 10% = 198% of 10000 = 19800
Hence, option E is correct.
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17. A certain amount of money amounts to Rs. 720 in 2 years and to Rs. 870 in 4(1/2) years. Find the rate of interest if S.l. is reckoned.




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Correct Ans:10%
Explanation:
Formula to find sum without rate of interest,
P = (A1*n2- A2*n1) / n2-n1
P = (720*9/2 - 870*2) / (9/2) -2
P = (3240 - 1740)/(5/2) = (1500*2)/5
P = 600
we know that,
SI = A - P
A = 720; P = 600
SI = 720 - 600 = 120
To find rate of interest
SI = Pnr/100
120 = (600*2*r)/100
Rate of interest, r = 10%
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18. If the difference between Cl and Sl earned on a certain amount at 15% pa at the end of 3 years is Rs.3200, find out the principal.




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Correct Ans:Rs.45150
Explanation:
The difference between Cl and Sl for 3 years = Pr²/100²[3 + (r/100)]
3200 = (P*15*15)/(100*100)[3 + (15/100)]
3200 = (P*3*3)/(20*20)[63/20]
P = 3200[(20*20*20)/(9*63)]
P = 45,149.91
P = 45,150
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19. A sum of money amounts to Rs. 1500 after 3 years and Rs. 2000 after 5 years at the same rate of SI. Find the rate of interest per annum ?




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Correct Ans:33.33%
Explanation:
We know that,
3 yr = 1500
5 yr = 2000
Then SI for 2 yrs (5yrs - 3 yrs) = 500
SI for 1 yr = 250
SI for 3 yrs = 250*3 = 750
P = A - SI
= 1500 - 750 = 750
SI = (P*N*R)/100
Therefore, R = (SI*100)/(P*N)
= (750*100)/(750*3) = 33.33%
Rate of interest = 33.33%
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20. A sum at simple interest of 13(1/2)% per annum amounts to Rs. 3080 in 4 years. Find the sum.




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Correct Ans:Rs. 2000
Explanation:
Given:
Amount - Rs. 3080; R = 27/2 %; N = 4 yrs
Let the sum be x.
SI = Amount - Principal
SI = 3080 - x
WKT, SI = PNR/100
3080 - x = (x * 27 * 4)/(100*2)
3080 - x = 27x/50
154000 - 50x = 27x
154000 = 27x + 50x
154000 = 77x
x = 154000/77
x = Rs. 2000
Therefore, sum is Rs. 2000.
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