Simple Interest(Quantitative Aptitude > Interest ) Questions and answers for exam Preparation

Quantitative Aptitude > Interest

SIMPLE INTEREST MCQs

Total Questions : 234 | Page 6 of 24 pages

Question 51. A borrows Rs.800 at the rate of 12% per annum simple interest and B borrows Rs.910 at the rate of 10% per annum, simple interest. In how many years will their amounts of debt be equal ?

20 years
18 years
24 years
22 years

Discuss Question

Answer: Option D. -> 22 years
Answer: (d)Using Rule 1,Let the period of time be T years.800 + ${800 × 12 × T}/100$= 910 + ${910 × 10 × T}/100$800 + 96 T = 910 + 91T96 T - 91 T = 910 - 8005T = 110T = $110/5$ = 22 years.

Question 52. The simple interest on a sum of money is $1/4$th of the principal and the number of years is equal to rate per cent per annum. The rate per cent is

5%
2.5%
10%
7.5%

Discuss Question

Answer: Option A. -> 5%
Answer: (a)Let the principal be x and rate be y% per annum.According to the question,SI = ${P × R × T}/100$$x/4 = {x × y × y}/100$$y^2 = 100/4$ = 25y = $√{25}$ = 5% per annumUsing Rule 5,n = $1/5$, R = TRT = n × 100$R^2 = 1/4 × 100$ = 25R = 5%

Question 53. 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 (In rupees) is

Discuss Question

Answer: Option B. -> 60
Answer: (b)Using Rule 1,Let first part be x and second part be(1750 –x )According to the question,x × $8/100 = (1750 - x ) × 6/100$8x + 6x = 1750 × 614x = 1750 × 6$x = {1750 × 6}/14$ = Rs.750Interest = 8% of 750= 750 × $8/100 = Rs.60

Question 54. In how many years will the simple interest on a sum of money be equal to the principal at the rate of 16$2/3$% per annum ?

5 years
4 years
8 years
6 years

Discuss Question

Answer: Option D. -> 6 years
Answer: (d)Using Rule 1,Let the principal be x.Time = $\text"SI × 100"/\text"Principal × Rate"$= ${x × 100 × 3}/{x × 50}$ = 6 years

Question 55. The difference between simple interest and the true discount on Rs. 2400 due 4 years hence at 5% per annum simple interest is

Rs.70
Rs.30
Rs.50
Rs.80

Discuss Question

Answer: Option D. -> Rs.80
Answer: (d)Using Rule 1,True discount= $\text"Amount × Rate × Time"/ \text"100 +(Rate × Time)"$= ${2400 × 5 × 4}/{100 + (5 × 4)}$= ${2400 × 5 × 4}/120$ = Rs.400S.I. = ${2400 × 5 × 4}/100$ = Rs.480Required difference= Rs.(480 - 400) = Rs.80

Question 56. Equal sum of money are lent to X and Y at 7.5% per annum for a period of 4 years and 5 years respectively. If the difference in interest, paid by them was Rs.150, the sum lent to each was

Rs.1000
Rs.500
Rs.3000
Rs.2000

Discuss Question

Answer: Option D. -> Rs.2000
Answer: (d)Let the sum lent be x.${x × 7.5 × 5}/100 - {x × 7.5 × 4}/100 = 150$${x × 7.5 × 1}/100$ = 150$x = {150 × 100}/{7.5}$ = Rs.2000Using Rule 13,Here, $P_1 = P, R_1 = 7.5%, T_1$ = 4 years.$P_2 = P, R_2 = 7.5%, T_2$ = 5 years.S.I. = Rs.150S.I. = ${P_2R_2T_2 - P_1R_1T_1}/100$150 = ${P × 7.5 × 5 - P × 7.5 × 4}/100$15000 = 7.5PP = $15000/{7.5}$P = $150000/75$ = Rs.2000

Question 57. A sum of Rs.1500 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 years is equal to that on another part at 12.5% per annum for 4 years. The sum lent out at 12.5% is :

Rs.1000
Rs.500
Rs.1250
Rs.750

Discuss Question

Answer: Option D. -> Rs.750
Answer: (d)Using Rule 1,Let the sum lent out at 12.5% be xSum lent out at 10% = 1500 - xNow, ${(1500 - x) × 10 × 5}/100$= ${x × 12.5 × 4}/100$50 (1500 - x ) = 50x2x = 1500$x = 1500/2$ = Rs.750

Question 58. Simple interest on Rs.500 for 4 years at 6.25% per annum is equal to the simple interest on Rs.400 at 5% per annum for a certain period of time. The period of time is

5 years
4 years
8$2/3$ years
6$1/4$ years

Discuss Question

Answer: Option D. -> 6$1/4$ years
Answer: (d)Using Rule 1,Let the period of time be T years. Then,${400 × 5 × T}/100 = {500 × 4 × 6.25}/100$T = ${500 × 4 × 6.25}/{400 × 5}$= $25/4 = 6{1}/4$ years

Question 59. The difference between the simple interest received from two different banks on Rs.500 for 2 years is Rs.2.50. The difference between their (per annum) rate of interest is :

0.25%
0.10%
1.00%
0.50%

Discuss Question

Answer: Option A. -> 0.25%
Answer: (a)${500 × 2 × R_1}/100 - {500 × 2 × R_2}/100$ = 2.5where $R_1 & R_2$ are rate% of both banks10 $(R_1 - R_2 )$ = 2.5$R_1 - R_2 = {2.5}/10$= 0.25 % per annum Using Rule 7If the difference between two simple interests is 'x' calculated at different annual rates and times, then principal (P) isP = $ {x × 100}/{(\text"difference in rate") ×(\text"difference in time")}$

Question 60. If the simple interest for 6 years be equal to 30% of the principal, it will be equal to the principal after

30 years
20 years
22 years
10 years

Discuss Question

Answer: Option B. -> 20 years
Answer: (b)Let the principal be P and rate of interest be r %According to the question,${30P}/100 = {P × R × 6}/100$30 = 6 RR = 5Now, let interest be equal to principal in T years.P = ${P × 5 × T}/100$T = $100/5$ = 20 years.Using Rule 5,Here, n = $30/100 = 3/10$, T = 6 years.RT = n × 100R × 6 = $3/10$ × 100R = 5%As,S.I. = PS.I. = ${P × R × T}/100$100 = RT100 = 5 × TThis is possible only when T = 20.