Practice Simple interest - quantitative aptitude Online Quiz (set-1) For All Competitive Exams

Q-1)   The simple interest on a sum of money is $8/25$ of the sum. If the number of years is numerically half the rate percent per annum, then the rate percent per annum is

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1
Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ or
S.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

Rate = R% per annum

Time = $R/2$ years

Rate = ${SI × 100}/\text"Principal × Time"$

R = $8/25 × 100/{R/2}$

$R^2 = {8 × 200}/25$ = 64

R = $√{64}$ = 8% per annum


Q-2)   A lent Rs.5000 to B for 2 years and Rs.3000 to C for 4 years on simple interest at the same rate of interest and received Rs.2200 in all from both as interest. The rate of interest per annum is

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

Let the rate of interest per annum be r%

According to the question,

${5000 × 2 × r}/100 + {3000 × 4 × r}/100 = 2200$

100r + 120r = 2200

220 r = 2200

r = $2200/220$ = 10%


Q-3)   A sum of Rs.1600 gives a simple interest of Rs.252 in 2 years and 3 months. The rate of interest per annum is:

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

Principal (P) = Rs.1600

T = 2 years 3 months

= $(2 + 3/12) yrs. = (2 + 1/4) yrs. = 9/4 yrs.$

S.I = Rs.252

R = % rate of interest per annum

R = ${100 × S.I.}/{P × t}$

= ${100 × 252}/{1600 × 9/4}$

Rate of interest = 7% per annum.


Q-4)   A sum of money amounts to Rs.5,200 in 5 years and to Rs.5,680 in 7 years at simple interest. The rate of interest per annum is

(a)

(b)

(c)

(d)

Explanation:

P + S.I. for 5 years = 5200 ..(i)

P + SI for 7 years = 5680 ...(ii)

On subtracting equation (i) from (ii),

SI for 2 years = 480

SI for 1 year = Rs.240

From equation (i),

P + 5 × 240 = 5200

P = 5200 - 1200 = Rs.4000

R = ${SI × 100}/{T × P}$

= ${240 × 100}/{1 × 4000}$ = 6%

Using Rule 12
If 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 = $({A_2T_1 - A_1T_2}/{T_1 - T_2})$

R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100

= $({5200 - 5680}/{5680 × 5 - 5200 × 7}) × 100$

= ${- 480}/{28400 - 36400}$ × 100

= ${- 480}/{- 8000} × 100$ = 6%


Q-5)   A sum of money at simple interest amounts to Rs.1,012 in 2$1/2$ years and to Rs.1,067.20 in 4 years. The rate of interest per annum is :

(a)

(b)

(c)

(d)

Explanation:

Principal + S.I. for $5/2$ years = Rs.1012 ...(i)

Principal + S.I. for 4 years = Rs.1067.20 ...(ii)

Subtracting equation (i) from (ii)

S.I. for $3/2$ years = Rs.55.20

S.I. for $5/2$ years

= $55.20 × 2/3 × 5/2$ = Rs.92

Principal

= Rs.(1012 - 92) = Rs.920

Rate = ${92 × 100}/{920 × 5/2}$

= ${2 × 92 × 100}/{920 × 5}$ = 4%

Using Rule 12,

R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100

= $({1012 - 1067.20}/{1067.20 × 5/2 - 1012 × 4}) × 100$

= ${- 55.2}/({2668 - 4048}) × 100$

= ${- 55.2}/{- 1380} × 100$ = 4%


Q-6)   The rate of simple interest for which a sum of money becomes 5 times of itself in 8 years is :

(a)

(b)

(c)

(d)

Explanation:

Principal = Rs.x (let)

Amount = Rs.5x

Interest = Rs.(5x - x) = Rs.4x

Rate = ${S.I. × 100}/\text"Principal × Time"$

= ${4x × 100}/{x × 8}$ = 50% per annum


Q-7)   If a sum of money doubles itself in 8 years, then the interest rate in percentage is

(a)

(b)

(c)

(d)

Explanation:

Let principal be Rs. x.

Amount = Rs.2x

Interest = Rs.(2x - x) = Rs.x

Rate = ${S.I. × 100}/\text"Principal × Time"$

= ${x × 100}/{x × 8} = 25/2$

= 12$1/2%$ per annum


Q-8)   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

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1
Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ or
S.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

${P × r × 1}/100 = {P × 5 × 2}/100$

[Since,Capital is same in both cases]

r × 1 = 5 × 2 = 10%


Q-9)   The present worth of a bill due 7 months hence is Rs.1200 and if the bill were due at the end of 2$1/2$ years its present worth would be Rs.1016. The rate per cent is

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1
Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ or
S.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

S.I. = ${\text"Principal × Rate × Time"/100$

1200 + ${1200 × 7 × r}/{12 × 100}$

= Amount (A)

1200 + 7r = A ...(i)

and, 1016 + ${1016 × 5 × r}/{2 × 100}$ = A

1016 + 25.4r = A ...(ii)

1016 + 25.4r = 1200 + 7r

25.4r - 7r = 1200 - 1016

18.4r = 184 ⇒ r = $184/{18.4}$

= 10% per annum


Q-10)   Ratio of the principal and the amount after 1 year is 10:12. Then the rate of interest per annum is :

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

$\text"Principal"/\text"Amount" = 10/12$

$\text"Amount"/ \text"Principal" = \text"Principal + interest"/ \text"Principal" = 12/10$

1 + $\text"Interest"/ \text"Principal" = 12/10$

$\text"Interest"/ \text"Principal" = 2/10 = 1/5$

Rate = $1/5$ × 100 = 20%


Q-11)   If the annual rate of simple interest increases from 10% to 12$1/2$% , a man's yearly income increases by Rs.1250. His principal (in rupees) is

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

Change in SI

= $(25/2 - 10)% = 5/2%$

$5/2$% of principal = Rs.1250

Principal = Rs.${1250 × 2 × 100}/5$ = Rs.50000


Q-12)   A sum of Rs. 800 amounts to Rs.920 in 3 years at the simple interest rate. If the rate is increased by 3% p.a., what will be the sum amount to in the same period ?

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

Case I,

S.I. = 920 - 800 = Rs.120

Rate = ${\text"S.I." × 100}/\text" Principal × Time"$

= ${120 × 100}/{800 × 3}$ = 5% per annum

Case II,

Rate = 8% per annum

S.I. = ${800 × 8 × 3}/100$ = Rs.192

Amount = Principal + S.I.

= (800 + 192) = Rs.992


Q-13)   The simple interest on a certain sum at 5% per annum for 3 years and 4 years differ by Rs.42. The sum is :

(a)

(b)

(c)

(d)

Explanation:

According to question,

Interest of one year = Rs.42

Rate = 5% and Time = 1 year

Principal = $\text"Interest × 100"/\text"Rate × Time"$

= ${42 × 100}/{5 × 1}$ = Rs.840

Using Rule 13
The 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 is
S.I. = ${P_2R_2T_2 - P_1R_1T_1}/100$

$P_1 = P, R_1 = 5%, T_1$ = 3years.

$P_2 = P, R_2 = 5%, T_2$ = 4 years.

S.I.= 42

42 = ${20P - 15P}/100$

P = 42 × 20 = Rs.840


Q-14)   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

(a)

(b)

(c)

(d)

Explanation:

$\text"Simple interest"/ \text"Principal" = 1/9$

If the annual rate of interest be r%, then

Rate = $\text"S.I. × 100"/ \text"Principal × Time"$

$r = 1/9 × 100/r$

$r^2 = 100/9$

r = $√{100/9} = 10/3 = 3{1}/3$%

Using Rule 5,

Here, n = $1/9$, R = T

RT = n × 100

$R^2 = 1/9 × 100 = 100/9$

R = $√{100/9} = 10/3 = 3{1}/3$%


Q-15)   In what time will Rs.72 become Rs.81 at 6$1/4$% per annum simple interest ?

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

Interest = Rs.(81–72)= Rs.9

Let the time be t years.

Then, 9 = ${72 × 25 × t}/{4 × 100}$

t = ${9 × 400}/{72 × 25}$ = 2 years.


Q-16)   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

(a)

(b)

(c)

(d)

Explanation:

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


Q-17)   Simple interest on a certain sum for 6 years is $9/25$ of the sum. The rate of interest is

(a)

(b)

(c)

(d)

Explanation:

Rate = ${\text"SI" × 100}/\text"Principal × Time"$

= $9/25 × 100/6$ = 6% per annum

Using Rule 5,

Here, n = $9/25$, T = 6 years.

R = ${n × 100}/T$

R = $9/25 × 100/6$

R = 6%


Q-18)   In what time will the simple interest be $2/5$ of the principal at 8 per cent per annum?

(a)

(b)

(c)

(d)

Explanation:

Let the principal be x

Interest = $2/5$ x

Rate = 8% per annum

Time = ${\text"Interest" × 100}/\text"Principal × Rate"$

=${{2/5}x × 100}/{x × 8} = 40/8$ = 5 years

Using Rule 5
If Simple Interest (S.I.) becomes 'n' times of principal i.e.
S.I. = P × n then.
RT = n × 100

Here, n = $2/5$ and R = 8%

RT = (n × 100)

T = ${n × 100}/R$

T = $2/5 × 100/8$ = 5 years


Q-19)   At the rate of simple interest per annum, the interest on a certain sum of money for 10 years will be $2/5$th part of the amount, then the rate of simple interest is

(a)

(b)

(c)

(d)

Explanation:

Amount after 10 years

= P$(1 + {RT}/100)$ = P$(1 + {R × 10}/100)$

= Rs. P$(1 + R/10)$

Interest = Rs.P$(1 + R/10) × 2/5$

Rate= ${\text"SI" × 100}/\text"Principal × Time"$

R = ${P(1 + R/10) × 2/5 × 100}/{P × 10}$

R = 4$(1 + R/10)$

$R/4 = 1 + R/10$

$R/4 - R/10$ = 1

${5R - 2R}/20$ = 1

3R = 20

R = $20/3 = 6{3}2%$

Using Rule 5,

Here, S.I. = $2/5$ amount

S.I. = $2/5$ (P + S.I.)

S.I. = $2/5$ S.I. + $2/5$ P

$3/5$ S.I. = $2/5$ P

S.I. = $2/3$P

Now, n = $2/3$, T = 10 years.

R= ${n × 100}/T$

= $2/3 × 100/10$

= $20/3 = 6{2}/3%$


Q-20)   In a certain time, the ratio of a certain principal and the simple interest obtained from it are in the ratio 10 : 3 at 10% interest per annum. The number of years the money was invested is

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

Time = $\text"S.I. × 100"/ \text"Principal × Rate"$

= $3/10 × 100/10$ = 3 years