## Quant Quiz On Simple Interest Day 16 Bag

• On a certain sum, the simple interest at the end of 5(1/3) years becomes 4/9 of the sum.What is the rate percent ?
A.5.5%
B.9.1%
C.7.6%
D.8.3%
E.10%

Explanation :
R = 100*(4x/9)  / (x*16/3)
R =100*4*3/9*16 = 100/12 = 8.3%
• P is going to pay Rs.700 to Q, 7 months later at 6% annual simple interest, Q is going to pay Rs.550 to P, 12 months later at 8% annual simple interest, if they decide to settle the debts, who will pay what amount to whom ?
A.A, Rs.149
B.B,Rs.167
C.A, Rs.155
D.B, Rs.197
E.None of these

Explanation :
For P:
P+ (p*6*7/12*100) = 700
1200p+42P = 700*1200
P = 676.33
For Q:
P+ (p*8*12/12*100) = 550
1200P+96P = 550*1200
P =509.26
Q =676-509 = 167
• A father left a will of Rs.5 lakhs between his two daughters aged 10 and 15 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.5 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?
A.Rs.2,04,797
B.Rs.3,05,890
C.Rs.1,90,00
D.Rs.4,00,700
E.Rs.2,46,870

Explanation :
Let Rs.x be the amount that the elder daughter got at the time of the will. Therefore, the younger daughter got (5,00,000 – x).
The elder daughter’s money earns interest for (21 – 15) = 6 years @ 10% p.a simple interest
The younger daughter’s money earns interest for (21 – 10) = 11 years @ 10% p.a simple interest.
As the sum of money that each of the daughters get when they are 21 is the same,
x + (6*10*x/100)= (5,00,000 – x) +(11*10*[5,00,000-x]/100)
100x+60x = (5,00,000-x)+(55,000,000-110x)
160x =55,500,000-111x
271x = 55,500,000
X = 2,04,797
• Two equal some of money were invested at an annual rate of 10%, One sum at simple interest and other at compound interest, If the difference between the interest after 2 years was Rs.100, What were the sum invested ?
A.25,000
B.100000
C.20,000
D.10,000
E.50,000

Explanation :
Assume X =100
SI = 120
CI = 121
100 mean difference 1
200 mean difference 2
Hence   10000 mean difference 100
• A man invests Rs.8000 for 5 years at 5% p.a. Simple Interest interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the fifth year.
A.Rs.10,500
B.Rs.10,500
C.Rs.9,600
D.Rs.10,000
E.None of these

Explanation :
5% is the rate of interest. 20% deducted mean rate of Interest 4%
SI = 8000*4*5/100=1600
The amount at the end of 5 years = 8000 + 1600 = 9600
• Ajay bought Rs.11,000 from a bank to buy a car at 12% simple Interest. If he paid \$ 6,600 as interest while clearing the loan, find the time for which the loan was given.
A.7
B.3
C.4
D.5
E.6

Explanation :
T = 6600/11000*0.12
T = 5
• Tarun invested an amount of Rs. 10000 at the simple interest rate of 8% per annum and another amount at the simple interest rate of 20% per annum. The total interest earned at the end of one year on the total amount invested became 12% per annum. Find the total amount invested.
A.Rs.12,000
B.Rs.15000
C.Rs.5,000
D.Rs.10,000
E.None of these

Explanation :
SI1= 10000*8*1/100 = 800
SI2 = x*20*1/100 = x/5
800+(x/5) = (10000+x)*12*1/100
80000+20x = 1,20,000+12x
8x = 40,000
X = 5000
Total= 10000+5000 = 15000
• If simple interest on a certain sum of money for 6 years at 5% per annum is same as the simple interest on Rs. 650 for 9 years at the rate of 12% per annum then the sum of money is
A.Rs.2340
B.Rs.3240
C.Rs.2400
D.Rs.3500
E.None of these

Explanation :
X *6*5/100 = 650*12*9/100
30x/100 = 70,200/100
30x = 70200
X = 2340
• Kailash borrowed some money at the rate of 5% p.a. for the first three years, 8% p.a. for the next five years and 11% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8800, how much money did he borrow?
A.Rs.7500
B.Rs.8000
C.Rs.9600
D.Rs.10,000
E.Rs.7,000

Explanation :
(x*5*3/100) + (x*8*5/100)+ (x*11*3/100 ) = 8800
15x/100 +40x/100 + 33x/100 = 8800
88x = 880000
X = 10000
• If the annual rate of simple interest increases from 8% to 13%, a man’s yearly income increases by Rs. 4800. His principal (in Rs.) is:
A.Rs.90,000
B.Rs.96,000
C.Rs.88,000
D.Rs.1,00,000
E.None of these

Explanation :
X*13*1/100  – x*8*1/100 = 4800
13x/100  –   8x/100 = 4800
5x/100 = 4800
5x = 480000
X = 96000

• Out of Rs. 60,000 that Rahul has, he lends Rs. 10,000 at 11/2 % per annum simple interest and Rs. 32,000 at 6% per annum simple interest. He lends the remaining money at a certain rate of interest so that he gets total annual interest of Rs. 4000. The rate of interest per annum, at which the remaining money is lent, is?
A.5%
B.7.5%
C.8%
D.8.5%
E.10%

Explanation :
Total Amount = 60000
Amount divided into three parts – x, y, z
x = 10000, T = 1 yr
SI(x) = (10000 * 11/2)/100 = 550
y = 32000 R = 6%
SI(y) = (32000 * 6)/100 = 1920
Total Interest = 4000, Interest on the remaining amount = 4000 – 550 – 1920 = 1530
z = 60000 – 32000 – 10000 = 18000
R = (1530 * 100) /18000 = 8.5%
• Vivek invests Rs 15000 as fixed deposit at a bank at the rate of 10% per annum SI. But due to some pressing needs he has to withdraw the entire money after 5 years, for which the bank allowed him a lower rate of interest. If he gets Rs 8250 less than what he would have got at the end of 10 years, the rate of interest allowed by the bank is
A.8%
B.8.5%
C.9%
D.9.5%
E.10%

Explanation :
P=15000, T1=10 years, T2=5 years, R1=10%, R2=?
[(15000*10*10)/100 – (15000*R2*5)/100] = 8250
15000 – 750R2 = 8250
R2 = 9%
• A father left a will of Rs.55 lakhs between his two sons aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.55 lakhs has been instructed to be invested at 10% p.a. SI. How much did the elder son get at the time of the will?
A.25 lakh
B.26 lakh
C.28 lakh
D.33 lakh
E.36 lakh

Explanation :
Let x be the amount of elder son at the time of will & Younger son’s amount at the time of will (550000 -x)
For elder son, T= 21-16=5
For younger son, T=21-8.5= 12.5
Amount Should be equal so,
x + [(x*10*5)/100] = (5500000-x) + [((5500000-x)*10*12.5)/100] 3x/2 = 12375000 – 2.25x
x=3300000
• Manish borrows 8000 at simple interest from a money lender. At the end of 3 years, he again borrows 7000 and closes his account after paying 8415 as interest after 8 years from the time he made the first borrowing. Find the rate of interest.
A.6%
B.6.5%
C.8%
D.8.5%
E.9%

Explanation :
Let x be the rate of interest
8000*3x/100 + 15000*5x/100 = 8415
240x + 750x = 8415
X = 8.5
• A portion of Rs.8500 is invested at a8% per annum, while the remainder is invested at a 3% per annum. If the annual income from the portion earning a 8% per annum is thrice that of the other portion, what is the total income from the two investments after one year?
A.Rs.350
B.Rs.370
C.Rs.450
D.Rs.480
E.Rs.520

Explanation :
8x + 3y = z (Total Income)
x + y = 8500 -(1)
8x= 3(3y)
8x – 9y = 0 -(2)
By solving (1) and (2) we get, x = 4500 so y = 4000
(4500*8*1)/100 + (4000*3*1)/100 = 360 + 120 = 480
• Raghu lends Rs 50,000 of two of his friends. He gives Rs 30,000 to the first at 6% p.a. simple interest. He wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is
A.8%
B.16%
C.11%
D.17%
E.19%

Explanation :
S.I. on Rs 30000
=(30000×6×1)/100 = Rs. 1800
Profit to made on Rs 50000
= 50000×10/100=Rs 5000
S.I.on Rs.20000 = 5000-1800 = Rs.3200
Rate=(S.I.* 100)/(P * T)=(3200×100)/20000
=16% per annum
Shortcut:
6……………………x
………..10…………….
3………………………2
4/(x-10)=2/3
x=16
• The rate of Simple Interest in SBI & BOB are in the ratio of 5:7. Gokul wants to deposit his total savings in two banks in such a way that he receive equal half-yearly interest from both banks.He should deposit in both banks SBI & BOB in the ratio of
A.4:5
B.7:5
C.9:5
D.8:5
E.5:9

Explanation :
R1 =5x; R2=7x; T1=T2=1/2 yr
[P1*5x*(1/2)]/100 = [P2*7x*(1/2)]/100
P1:P2 = 7:5
• Vinay borrowed some money for one year at 8% per annum simple interest and after 18 months , he again borrowed the same money at a Simple Interest of 32% per annum. In both the cases, he paid Rs.5452. Which of the following could be the amount that was borrowed by Hari in each case if interest is paid half yearly?
A.3900
B.4200
C.4500
D.4700
E.None of the Above

Explanation :
16% for 6 months
x = Borrowed money
Take x =100%
116% of x = 5452
x = 4700
• Ravi borrows a sum of Rs.2000 at the beginning of a year. After four months Rs.2600 more is borrowed at a rate of interest double the previous one. At the end of one year, the sum of interest on both the loans is Rs.494. What is the first rate of interest per annum?
A.8.5%
B.9%
C.9.5%
D.12%
E.None of the Above

Explanation :
P = 2000
Rate of Interest = x
SI = 2000x/100 = 20x
P = 2600
Rate of Interest = 2x
SI = 5200x/100 = 52x
52x = 494
x = 9.5%
• Kumar fixes the rate of interest 5% per annum for first 3 years and for the next 4 years 6 percent per annum and for the period beyond 7 years, 7.5 percent per annum. If Mr. Kumar lent out Rs.1800 for 11 years, find the total interest earned by him?
A.Rs.1422
B.Rs.1242
C.Rs.1244
D.Rs.1342
E.None of the Above

Explanation :
5% for 3 years = 15%
6% for 4 years = 24%
7.5% for 4 years = 30%
69% of 1800 = 1242

• Vikram invests some money in three different schemes for 4 years, 8 years and 12 years at 10%, 15% and 20% Simple Interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investments is
A. 6 : 2 : 1
B. 5 : 2 : 1
C. 5 : 2 : 3
D. 5 : 2 : 7
E. None of the Above

A. 6 : 2 : 1
Explanation:
Principal = x1, x2 and x3
x1 * 4 * 10 = x2 * 8 * 15 = x3 * 12 * 20
x1 = 3×2 = 6×3
x1 : x2 = 3 : 1 ; x2 : x3 = 2 : 1
x1 : x2 : x3 = 6 : 2 : 1
• Mr. Ravi finds that due to a fall in the rate of interest from 9% to 6%, his yearly income diminishes by Rs.267. His capital is ?
A. Rs.3800
B. Rs.8400
C. Rs.8600
D. Rs.8900
E. None of the Above

D. Rs.8900
Explanation:
Difference in Rate of Interest = 9% – 6% = 3%
Capital = x
3% of x = 267
x = 8900
• Out of Rs. 50,000 that a man has, he lends Rs. 8,000 at 11/2 % per annum simple interest and Rs. 24,000 at 6% per annum simple interest. He lends the remaining money at a certain rate of interest so that he gets total annual interest of Rs. 3,680. The rate of interest per annum, at which the remaining money is lent, is ?
A. 5%
B. 7%
C. 10%
D. 12%
E. None of the Above

C. 10%
Explanation:
Total Amount = 50000
Amount divided into three parts – x, y, z
x = 8000, T = 1 yr
SI(x) = (8000 * 11/2)/100 = 440
y = 24000 R = 6%
SI(y) = (24000 * 6)/100 = 1440
Total Interest = 3680, Interest on the remaining amount = 3680 – 440 – 1440 = 1800
z = 50000 – 24000 – 8000 = 18000
R = (1800 * 100) /18000 = 10%
• Vikram lends Rs 30,000 of two of his friends. He gives Rs 15,000 to the first at 6% p.a. simple interest. He wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is
A. 8%
B. 16%
C. 12%
D. 14%
E. None of the Above

D. 14%
Explanation:
S.I. on Rs 15000
=(15000×6×1)/100 = Rs. 900
Profit to made on Rs 30000
= 30000×10/100=Rs 3000
S.I.on Rs.15000 = 3000-900 = Rs.2100
Rate=(S.I.* 100)/(P * T)=(2100×100)/15000
=14% per annum
• Suresh lends 40% of his money at 15% per annum, 50% of the rest at 10% per annum and the rest at 18% per annum rate of interest. What would be the annual rate of interest, if the interest is calculated on the whole sum?
A. 18.5%
B. 14.4%
C. 16.5%
D. 19.5%
E. None of the Above

B. 14.4%
Explanation:
x – (40/100)*x = 60x/100
40/100 at 15% p.a = 40/100 * 15/100 = 60x/1000
50/100*60x/100 = 30x/100 at 10% p.a = 30x/100 * 10/100 = 30x/1000
Balance amount = x – 40x/100 – 30x/100 = 30x/100 at 18% p.a = 18/100 * 30x/100 = 54x/1000
R = [(144x/1000)/x] * 100 = 14.4%
• Ajay borrows Rs 1000 at the rate of 12% per annum simple interest and Babu borrows Rs 1050 at the rate of 10% per annum simple interest. In how many years will their amounts of debts be equal?
A. 18/5
B. 10/3
C. 22/3
D. 10/5
E. None of the Above

B. 10/3
Explanation:
Let Time = x years Then,
[1000+(1000*12*x)/100] = [1050+(1050*10*x)/100] => 1000 + 120x = 1050 + 105x
=> 15x = 50 ⇒ x = 10/3 years
• A sum of Rs. 8800 is to be divided among three brothers Anil, Deepak and Ramesh in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 year respectively remains equal. The share of Anil is more than that of Ramesh by?
A. Rs. 3200
B. Rs. 2500
C. Rs. 3000
D. Rs. 2700
E. None of the Above

A. Rs. 3200
Explanation:
x*5*1/100 = y*5*2/100 = z*5*3/100
x:y:z = 6:3:2
The share of Anil is more than that of Ramesh by = 4/11 * 8800 = 3200
• Mayank invested a certain sum of money in a simple interest bond, that value grew to Rs. 300 at the end of 3 year and to Rs. 400 at the end of another 5 year. Then what was the rate of interest in which he invested his sum?
A. 12%
B. 12.5%
C. 6.67%
D. 8.33%
E. None of the Above

D. 8.33%
Explanation:
P*R*3/100 + P = 300 –(i)
P*R*8/100 + P = 400 –(ii)
From (i) and (ii)
P*R*5/100 = 100
P*R = 2000—(iii)
Sub (iii) in (i)
6000/100 + P = 300
P = 240
240*R = 2000 => R = 8.33%
• Vivek took a loan from the bank at 8% per annum, and was supposed to pay a sum of Rs.2500 at the end of 4 years. If the same sum is cleared off in four equal annual instalments at the same rate, then the amount of annual instalment will be?
A. Rs.558
B. Rs.978
C. Rs.766
D. Rs.856
E. None of the Above

A. Rs.558
Explanation:
x + (x*8*1/100) = 27x/25
x + (x*8*2/100) = 29x/25
x + (x*8*3/100) = 31x/25
(x + 27x/25 + 29x/25 + 31x/25) = 2500
112x/25 = 2500 => x = 558
• Sachin invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest. He received yearly interest of Rs.140. But if he had interchanged the amounts invested, he would have received Rs.4 more as interest. How much did he invest at 12% simple interest?
A. Rs. 750.65
B. Rs. 545.45
C. Rs. 850.65
D. Rs. 465.45
E. None of the Above

B. Rs. 545.45
Explanation:
Amount invested at 12% = Rs. x
Amount invested at 10% = Rs. y
140 = x*12*1/100 + y*10*1/100
12x + 10y = 14000 -(i)
144 = x*10*1/100 + y*12*1/100
10x + 12y = 14400 -(ii)
x = 545.45

• Bharat borrowed Rs.180,000 on a condition that he had to pay 7.5% interest every year. He also agreed to pay the principal in equal annual instalments over 21 years. After a certain number of years, however, the rate of interest has been reduced to 7%. It is also known that at the end of the agreed period, he will have paid in all Rs.2,70,900 in interest. For how many years does he pay at the reduced interest rate?
A. 10 years
B. 12 years
C. 13 years
D. 14 years
E. None of the Above

D. 14 years
Explanation:
x = interest paid at 7.5%
(21-x) years interest paid at 7%
((180000*x*7.5)/100) + ((180000*7*(21-x))/100) = 270900
x = 7
21 – 7 = 14 years he paid at the reduced interest rate.
• Ankita borrows Rs.7000 at simple Interest from a lender. At the end of 3 years, she again borrows Rs.3000 and settled that amount after paying Rs.4615 as interest after 8 years from the time she made the first borrowing. what is the rate of interest?
A. 5.5%
B. 9.5%
C. 7.5%
D. 6.5%
E. None of the Above

D. 6.5%
Explanation:
SI for Rs.7000 for 8 years= (7000*r*8)/100
Again borrowed=3000
SI = (3000*r*5)/100
Total interest= [(7000*r*8)/100] + [(3000*r*5)/100] = 4615
560r + 150r = 4615
710r = 4615
r = 6.5%
• Hari borrowed some money for one year at 6% per annum simple interest and after 18 months , he again borrowed the same money at a Simple Interest of 24% per annum. In both the cases, he paid Rs.4704. Which of the following could be the amount that was borrowed by Hari in each case if interest is paid half yearly?
A. 4000
B. 3000
C. 4400
D. 4200
E. None of the Above

D. 4200
Explanation:
12% for 6 months
x = Borrowed money
Take x =100%
112% of x = 4704
x = 4200
• Ravi lent out a part of Rs. 38800 is lent out at 6% per six months. The rest of the amount is lent out at 5% per annum after one year. The ratio of interest after 3 years from the time when first amount was lent is 5:4. Find the second part that was lent out at 5%.
A. 28500
B. 30080
C. 20500
D. 28800
E. None of the Above

D. 28800
Explanation:
First Part = x
[x * (0.06)*6] / (388800 – x)*0.05*2 = 5/4
1.44x = 19400 – 0.5x
x = 10000
Second Part = 38800 – 10000 = 28800
• Harshita lent out some money at 6% Simple Interest per annum. After one year, Rs.6800 is repaid and the rest of the amount is repaid at 5% per annum. If the second year’s interest is 11/20 of the first year’s interest, find what amount of money was lent out.
A. 18500
B. 10080
C. 17000
D. 18000
E. None of the Above

C. 17000
Explanation:
P – amount lent by Harshita
I=.06*P —(i)
The interest for second year as X=(P+I-6800).05 —(ii)
x=(11/20)I —(iii)
Put (i) in (ii) and (iii)
P = 17,000
• Vikram borrows a sum of Rs.1500 at the beginning of a year. After four months Rs.2100 more is borrowed at a rate of interest double the previous one. At the end of one year, the sum of interest on both the loans is Rs.416. What is the first rate of interest per annum?
A. 5.5%
B. 4.5%
C. 6.7%
D. 7.3%
E. None of the Above

D. 7.3%
Explanation:
P = 1500
Rate of Interest = x
SI = 1500x/100 = 15x
P = 2100
Rate of Interest = 2x
SI = 4200x/100 = 42x
57x = 416
x = 7.3%
• Rahul invested a sum of money at Simple Interest at a certain rate of interest for three years. Had it been invested at a 4% higher rate, it would have fetched Rs.480 more. Find out the Principal amount that was invested by Rahul?
A. 3000
B. 4000
C. 5000
D. 4500
E. None of the Above

B. 4000
Explanation:
x – Principal
Extra amount = 4% for 3 years = 12% of x = 480
x = (480/12)*100 = 4000
• Rakesh fixes the rate of interest 6% per annum for first 3 years and for the next 4 years, 7 percent per annum and for the period beyond 7 years, 7.5 percent per annum. If Mr. Rakesh lent out Rs.1500 for 11 years, find the total interest earned by him?
A. Rs.1100
B. Rs.1200
C. Rs.1140
D. Rs.1350
E. None of the Above

C. Rs.1140
Explanation:
6% for 3 years = 18%
7% for 4 years = 28%
7.5% for 4 years = 30%
76% of 1500 = 1140
• An equal amount of sum is invested in two schemes for four years each, both offering simple interest. When invested in scheme A at 8% per annum the sum amounts to Rs.5280. In scheme B, invested at 12% per annum it amounts to Rs.5920. What is the total sum invested?
A. 5000
B. 9000
C. 7000
D. 8000
E. None of the Above

D. 8000
Explanation:
Sum = x
x + [(x*4*8)/100] = 5280
33x = (5280*25) = 4000
Total sum = 2 * 4000 = 8000
• Simple Interest on a certain sum at a certain annual rate of interest is 16% of the sum. If the numbers representing rate per cent and time in years be equal, then the rate of interest is?
A. 2%
B. 4%
C. 6%
D. 8%
E. None of the Above