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 78 of 118 pages

Question 771. If x, y, z are three sum of money such that y is the simple interest on x and z is the simple interest on y for the same time and at the same rate of interest, then we have

$xyz$ = 1
$z^2 = xy$
$y^2 = zx$
$x^2 = yz$

Discuss Question

Answer: Option C. -> $y^2 = zx$
Answer: (c)Using Rule 1,S.I. = ${P × R × T}/100$$y = {x × T × R}/100$and $z = {y × T × R}/100$So, $y/z = x/y = ⇒ y^2 = zx$

Question 772. The simple interest on Rs.4,000 in 3 years at the rate of x% per annum equals the simple interest on Rs.5,000 at the rate of 12% per annum in 2 years. The value of x is

Discuss Question

Answer: Option B. -> 10%
Answer: (b)Using Rule 1,S.I. = ${\text"Principal × Rate × Time"/100$${4000 × 3 × x}/100$= ${5000 × 2 × 12}/100$$x = {5 × 2 × 12}/{4 × 3}$= 10% per annum

Question 773. The difference between the simple interest received from two different sources on Rs.1500 for 3 years is Rs.13.50. The difference between their rates of interest is:

0.2%
0.1%
0.4%
0.3%

Discuss Question

Answer: Option D. -> 0.3%
Answer: (d)Let $r_1$, and $r_2$ be the required rate of interestThen, ${13.50} = {1500 × 3 × r_1}/100$– ${1500 × 3 × r_2}/100 = 4500/100(r_1 - r_2)$$r_1 - r_2 = 135/450 = 27/90$= $3/10$ = 0.3%Using Rule 13,$P_1 = Rs.1500, R_1 , T_1$ = 3 years.$P_2 = Rs.1500, R_2 , T_2$ = 3 years.S.I. = Rs.13.5013.50 = ${1500 × R_2 × 3 - 1500 × R_1 × 3}/100$$1350/100 = {4500(R_2 - R_1)}/100$$R_2 - R_1 = 1350/4500 = 27/90$= $3/10$ = 0.3%

Question 774. The simple interest on a sum of money is $1/9$ of the principal and the number of years is equal to rate per cent per annum. The rate per annum is

$1/3$%
3%
$3/10$%
3$1/3$%

Discuss Question

Answer: Option D. -> 3$1/3$%
Answer: (d)$\text"Simple interest"/ \text"Principal" = 1/9$If the annual rate of interest be r%, thenRate = $\text"S.I. × 100"/ \text"Principal × Time"$$r = 1/9 × 100/r$$r^2 = 100/9$r = $√{100/9} = 10/3 = 3{1}/3$%Using Rule 5,Here, n = $1/9$, R = TRT = n × 100$R^2 = 1/9 × 100 = 100/9$R = $√{100/9} = 10/3 = 3{1}/3$%

Question 775. 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 :

Rs.2400
Rs.2,580
Rs.3600
Rs.2529

Discuss Question

Answer: Option C. -> Rs.3600
Answer: (c)Let the sum be x${x × 5 × 15}/{100 × 12} - {x × 4 × 8}/{100 × 12}$ = 129$x/{100 × 12}$(75 - 32) = 129$x = {129 × 1200}/43$ = Rs.3600Using Rule 13,$P_1 = P, R_1 = 4%$$T_1 = 8 months = 8/12$ years$P_2 = P, R_2$ = 5%$T_2 = 15 month = 15/12$ yearsS.I. = Rs.129129 = ${P × 5 × 15/12 - P × {4 × 8}/12}/100$12900 = ${75P - 32P}/12$12900 = ${43P}/12$P = Rs.3600

Question 776. 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 777. 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 778. 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 779. 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 780. 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