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

Quantitative Aptitude > Interest

SIMPLE & COMPOUND INTEREST MCQs

Compound Interest, Simple Interest, Interest (combined)

Total Questions : 1171 | Page 77 of 118 pages

Question 761. A sum of money lent at simple interest amounts to Rs.880 in 2 years and to Rs.920 in 3 years. The sum of money (in rupees) is

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Answer: Option C. -> 800
Answer: (c)If the principal be x and rate of interest be r% per annum, thenSI after 1 year = 920 - 880 = Rs.40SI after 2 years = Rs.80880 = x + 80x = Rs.(880 - 80) = Rs.800Using Rule 12If certain sum P amounts to Rs. $A_1$ in $t_1$ years at rate of R% and the same sum amounts to Rs. $A_2$ in $t_2$ years at same rate of interest R%. Then,(i) R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100(ii) P = $({A_2T_1 - A_1T_2}/{T_1 - T_2})$

Question 762. Ram deposited a certain sum of money in a company at 12% per annum simple interest for 4 years and deposited equal amount in fixed deposit in a bank for 5 years at 15% per annum simple interest. If the difference in the interest from two sources is Rs.1350, then the sum deposited in each case is :

Rs.4000
Rs.3000
Rs.6500
Rs.5000

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Answer: Option D. -> Rs.5000
Answer: (d)Let amount invested in each company be Rs. x.S.I. = ${\text"Principal × Rate × Time"/100$According to the question,${x × 15 × 5}/100 - {x × 12 × 4}/100$ = 1350${75x}/100 - {48x}/100$ = 1350${27x}/100$ = 1350$x = {1350 × 100}/27$ = Rs. 5000Using Rule 13Here, $P_1 = Rs. P, R_1 = 12%, T_1$ = 4 years$P_2 = Rs. P, R_2 = 15%, T_2$ = 5 yearsS.I. = Rs. 1350S.I.= ${P_2R_2T_2 - P_1R_1T_1}/100$1350 = ${P × 15 × 5 - P × 12 × 4}/100$135000 = 75 P - 48P135000 = 75 PP = Rs. 5000

Question 763. Simple interest on a certain sum at a certain annual rate of interest is $16/25$ of the sum. If the number representing rate per cent and time in years be equal, then the rate of interest is

11$1/2$%
8%
12$1/4$%
12$1/2$%

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Answer: Option B. -> 8%
Answer: (b)Let the rate of interest be r% and principal be P.According to the question.${16P}/25 = {P × r × r}/100$[Since, r = t numerically]$r^2 = 1600/25$r = $40/5$ = 8 % Using Rule 5If Simple Interest (S.I.) becomes 'n' times of principal i.e.S.I. = P × n then.RT = n × 100

Question 764. The rate of interest per annum at which the total simple interest of a certain capital for 1 year is equal to the total simple interest of the same capital at the rate of 5% per annum for 2 years, is

10%
$5/2$%
12.5%
25%

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Answer: Option A. -> 10%
Answer: (a)Using Rule 1Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ orS.I. = ${\text"P × R × T"/100$P = ${\text"S.I." × 100}/\text"R × T"$, R = ${\text"S.I." × 100}/\text"P × T"$, T = ${\text"S.I." × 100}/\text"P × R"$ A = P + S.I. or S.I. = A - P

Question 765. Prakash lends a part of Rs.20,000 at 8% simple interest and remaining at $4/3$% simple interest. His total income after a year was Rs.800. Find the sum lent at 8%.

Rs.12,000
Rs.8,000
Rs.10,000
Rs.6,000

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Answer: Option B. -> Rs.8,000
Answer: (b)Using Rule 1,Amount lent at 8% rate of interest = Rs.xAmount lent at $4/3$% rate of interest = Rs.(20,000 - x)S.I. = ${\text"Principal × Rate × Time"/100$${x × 8 × 1}/100 + {(20,000 - x) × 4/3 × 1}/100$ = 800${2x}/25 + {20,000 - x}/75 = 800$${6x + 20,000 - x}/75 = 800$5x + 20,000 = 75 × 800 = 60,0005x = 60,000-20,000 = 40,000$x = {40,000}/5$ = Rs.8000

Question 766. The simple interest on a sum of money is $4/9$ of the principal and the number of years is equal to the rate percent per annum. The rate per annum is :

6$2/3$%
5%
7$1/5$%
6%

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Answer: Option A. -> 6$2/3$%
Answer: (a)Using Rule 1Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ orS.I. = ${\text"P × R × T"/100$P = ${\text"S.I." × 100}/\text"R × T"$, R = ${\text"S.I." × 100}/\text"P × T"$, T = ${\text"S.I." × 100}/\text"P × R"$ A = P + S.I. or S.I. = A - P

Question 767. A person deposited Rs.500 for 4 years and Rs.600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs.190 as interest. The rate of simple interest per annum was

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Answer: Option A. -> 5%
Answer: (a)Using Rule 1,Let 'r' be the rate of interest190 = ${500 × 4 × r}/100 + {600 × 3 × r}/100$20r + 18r = 19038r = 190r = $190/38$ = 5%

Question 768. The simple interest on a sum of money is $1/16$ of the principal and the number of years is equal to the rate per cent per annum. The rate per annum is

2$1/2$%
1$1/2$%
4$1/2$%
3$1/2$%

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Answer: Option A. -> 2$1/2$%
Answer: (a)Let the annual rate of interest = r%Time = r yearsLet the principal be x .Interest = $x/16$According to the question,$x/16 = {x × r × r}/100$ [Since, r = t]16$r^2$ = 100$r^2 = 100/16 = 25/4$r = $√ {25/4} = 5/2 = 2{1}/2$%Using Rule 5,Here, n = $1/16$, R = TRT = n × 100$R^2 = 100/16$R = $√{100/16} = 10/4 = 2{1}/2%$

Question 769. The simple interest on a certain sum at 5% per annum for 3 years and 4 years differ by Rs.42. The sum is :

Rs.280
Rs.210
Rs.840
Rs.750

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Answer: Option C. -> Rs.840
Answer: (c)According to question,Interest of one year = Rs.42Rate = 5% and Time = 1 yearPrincipal = $\text"Interest × 100"/\text"Rate × Time"$= ${42 × 100}/{5 × 1}$ = Rs.840 Using Rule 13The difference between the S.I. for a certain sum $P_1$ deposited for time $T_1$ at $R_1$ rate of interest and another sum $P_2$ deposited for time $T_2$ at $R_2$ rate of interest isS.I. = ${P_2R_2T_2 - P_1R_1T_1}/100$

Question 770. If Rs.12,000 is divided into two parts such that the simple interest on the first part for 3 years at 12% per annum is equal to the simple interest on the second part for 4$1/2$ years at 16% per annum, the greater part is

Rs.6,000
Rs.8,000
Rs.7,500
Rs.7,000

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Answer: Option B. -> Rs.8,000
Answer: (b)Using Rule 1,Let the larger part of the sum be xSmaller part = Rs.(12000 - x)According to the question,${x × 3 × 12}/100 = {(12000 - x) × 9 × 16}/{2 × 100}$36 x = (12000 - x ) 72x = (12000 - x ) × 2x + 2x = 240003x = 24000$x = 24000/3$ = Rs.8000