Practice Difference equality in si rate years - quantitative aptitude Online Quiz (set-1) For All Competitive Exams

Q-1)   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

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

Let 'r' be the rate of interest

190 = ${500 × 4 × r}/100 + {600 × 3 × r}/100$

20r + 18r = 190

38r = 190

r = $190/38$ = 5%

Q-2)   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

(a)

(b)

(c)

(d)

Explanation:

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

Q-3)   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

(a)

(b)

(c)

(d)

Explanation:

Let the principal be x and rate be y% per annum.

According to the question,

SI = ${P × R × T}/100$

$x/4 = {x × y × y}/100$

$y^2 = 100/4$ = 25

y = $√{25}$ = 5% per annum

Using Rule 5,

n = $1/5$, R = T

RT = n × 100

$R^2 = 1/4 × 100$ = 25

R = 5%

Q-4)   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

(a)

(b)

(c)

(d)

Explanation:

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 × 6

14x = 1750 × 6

$x = {1750 × 6}/14$ = Rs.750

Interest = 8% of 750

= 750 × $8/100 = Rs.60

Q-5)   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-6)   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:

(a)

(b)

(c)

(d)

Explanation:

Let $r_1$, and $r_2$ be the required rate of interest

Then, ${13.50} = {1500 × 3 × r_1}/100$

– ${1500 × 3 × r_2}/100 = 4500/100(r_1 - r_2)$

$r_1 - r_2 = 135/450 = 27/90$

= $3/10$ = 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.13.50

13.50 = ${1500 × R_2 × 3 - 1500 × R_1 × 3}/100$

$1350/100 = {4500(R_2 - R_1)}/100$

$R_2 - R_1 = 1350/4500 = 27/90$

= $3/10$ = 0.3%

Q-7)   The difference between simple interest and the true discount on Rs. 2400 due 4 years hence at 5% per annum simple interest is

(a)

(b)

(c)

(d)

Explanation:

Using Rule 1,

True discount

= $\text"Amount × Rate × Time"/ \text"100 +(Rate × Time)"$

= ${2400 × 5 × 4}/{100 + (5 × 4)}$

= ${2400 × 5 × 4}/120$ = Rs.400

S.I. = ${2400 × 5 × 4}/100$ = Rs.480

Required difference

= Rs.(480 - 400) = Rs.80

Q-8)   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 :

(a)

(b)

(c)

(d)

Explanation:

${500 × 2 × R_1}/100 - {500 × 2 × R_2}/100$ = 2.5

where $R_1 & R_2$ are rate% of both banks

10 $(R_1 - R_2 )$ = 2.5

$R_1 - R_2 = {2.5}/10$

= 0.25 % per annum

Using Rule 7
If the difference between two simple interests is 'x' calculated at different annual rates and times, then principal (P) is
P = $ {x × 100}/{(\text"difference in rate") ×(\text"difference in time")}$

Here, P = Rs. 500, x = Rs. 2.50

Difference in time = 2 years.

Difference in rate = ?

500 = ${2.50 × 100}/{(\text"diff.in rate") × 2}$

Different in rate = 0.25%

Q-9)   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-10)   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 = $√{100/9} = 10/3 = 3{1}/3$%