Aptitude Questions : Simple Interest Set 1

Q.1) Graham lent sum of Rs.840 to Rajesh in the beginning of the year at a certain rate of interest. After 6 months Rs.420 is lent to the same person but the rate of interest is twice the former. At the end of the year Rs.80 is earned as total interest by graham then what is the original rate of interest.

(a) 7.85%

(b) 5.45%

(c) 6.34%

(d) 7.46%

(e) 5.64%

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c

SI=PNR/100

Since the second loan is given after 6 months n=1/2

(840×R×1)/100+(420×2R×1)/(100×2)=80

8.4 R + 4.2 R=80

12.6 R=80

R=80/12.6

=6.34%

Q.2) What annual instalment will discharge a debt of Rs.1053 due in 3 years at 8% simple interest?

(a) 324

(b) 325

(c) 320

(d) 330

(e) 328

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b

Let x be the instalment

For 1st year=x+(x×8×1)/100
For 2nd year=x+(x×821)/100
For 3rd year=x

[x+(x×8×1)/100]+[x+(x×8×2)/100]+x=1053

3x + 16x/100+8x/100=105
300x+24x=105300

324x=105300

x=325

Q.3) Stokes gave a loan of Rs. 400 to Rashid and recovered it at the rate of Rs. Rs.100 each month for six months, commencing from the end of 1st month. What is the effective rate of simple interest per annum?

(a) 115%

(b) 100%

(c) 95%

(d) 80%

(e) 50%

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b
Principal = Rs.400
Amount = Rs 100 x 6 = Rs 600
Interest = Rs 600 – Rs 400 = Rs 200
Time = 6 months =  6/12  years
200=  (400×1×r)/(2×100)
r =  (440×100)/400

=100%

Q.4)  Find the amount of equal instalment, annual payment of which will discharge a debt of Rs. 406 due in 2 years at 3% p.a. of Simple interest.

(a) 240

(b) 234

(c) 334

(d) 200

(e) 340

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d
Amount of each installment = (100 p)/(100n+(n(n-1)r)/2)
(100 ×406)/(100×2+2(2-1)3/2)

=40600/203=200

=Rs.200

Q.5) Find the amount of debt that will be discharged by equal installments of Rs. 150 each, if the debt is due in 4 year at 2% p.a.

(a) 618

(b) 634

(c) 674

(d) 650

(e) 640

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a

Amount of each installment  = (100 p)/(100n+n(n-1)r/2)

150= (100 p)/(100×4+4(4-1)2/2)

150= (100 p)/(400+12)

p=150/100 (412)=618

=Rs.618

Q.6) Vidal borrows Rs. 50,000 from a bank at 5% p.a. simple interest and clears the debt in five years. If the installments paid at the end of the first, second, third and fourth years to clear the debt are Rs. 5,000, Rs. 10,000, Rs. 15,000 and Rs. 20,000 respectively, what amount should be paid at the end of the fifth year to clear the debt?

(a) Rs 8,000

(b) Rs 7,500

(c) Rs 7,000

(d) Rs 5,900

(e) Rs 6,000

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b

In the case of simple interest, instalment amount will always be reduced from principal and the interest will be calculated on the remaining principal.

Simple interest for 1st yr=pnr/100=(50000×1×5)/100=2500

Amount after 1st instalment=50000-5000=45000

Simple interest for 2nd yr=pnr/100=(45000×1×5)/100=2250

Amount after 2nd instalment=45000-10000=35000

Simple interest for 3rd yr=pnr/100=(35000×1×5)/100=1750

Amount after 3rd instalment=35000-15000=20000

Simple interest for 4th yr=pnr/100=(20000×1×5)/100=1000

Amount after 4th instalment=20000-20000=0

Balance of debt for the fifth year=2500+2250+1750+1000=7500

Q.7) The simple interest on a sum of money will be Rs.900 after 8 years. If the principal is tripled for the last 4 years, what will be the total interest at the end of the 8th year?

(a) Rs.600

(b) Rs.900

(c) Rs.1200

(d) Rs.1800

(e) Data inadequate

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d

Let sum be x
n=8 yrs
SI=900
R=(100×SI)/(P×n)

R=(100×900)/(x×8)=11250/x

For 1st 4 yrs

SI=(x×11250/x×4×1/100)=450

For last 4 yrs

SI=(3x×11250/x×4×1/100)=1350

Total interest=1350+450=1800

Q.8) A certain sum of money at simple interest amounts to Rs.1100 in 3 years and to Rs.1460 in 6 years. The rate percent per annum is:

(a) 27%

(b) 16%

(c) 25%

(d) 11%

(e) 34%

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b
S.I for 3 years = Rs.(1460-1100)=Rs.360

Sum = Rs.(1100-360) = Rs.740
Rate =  (100×240)/(740×2)=16.21%≈16%

 

Q.9)  Two equal amounts of money are deposited in two banks, each at 9% per annum, for 4  1/2  and 6  1/2  years. If the difference between their interests is Rs.288, each sum is:

(a) Rs.1600

(b) Rs.1500

(c) Rs.1640

(d) Rs.1720

(e) Rs.1540

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a
Let each sum be Rs. P. Then,
(p×9×13)/(100×2)-(p×9×9)/(100×2)=288
117P/200-81P/200=36P/200=288
P=(288×200)/36=1600

Q.10) Rajesh has a total of Rs.42,000. And in that, he lends Rs.8,000 at 9/2% per annum simple interest and Rs.12,000 at 8% per annum simple interest. He lends the remaining money at a certain rate of interest so that he gets total interest of Rs. 3600 at the end of one year. The rate of interest per annum, at which the remaining money is lent, is?

(a) 11.50%

(b) 10.36%

(c) 8.54%

(d) 9.65%

(e) 12.24%

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b

For first loan
SI=PNR/100

=(8000×9×1)/(100×2)=360

For Second loan=(12000×8×1)/100=960

Total interest=3600

So for the third loan SI=3600-(960+360)=2280

Rate of interest for third loan=(2280×100)/22000=10.36%

 

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