type 4 difference & equality of si rate & years Practice Questions Answers Test with Solutions & More Shortcuts

Question : 16 [SSC CPO S.I.2009]

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) 5%

b) 2.5%

c) 10%

d) 7.5%

Answer: (a)

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

According to the question,

SI = ${P × R × T}/100$

$x/4 = {x × y × y}/100$

$y^2 = 100/4$ = 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%

Question : 17 [SSC CGL Prelim 2002]

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) 65

b) 60

c) 40

d) 70

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 × 6

14x = 1750 × 6

$x = {1750 × 6}/14$ = Rs.750

Interest = 8% of 750

= 750 × $8/100 = Rs.60

Question : 18 [SSC CPO S.I.2009]

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

a) Rs.1000

b) Rs.500

c) Rs.3000

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.2000

Using 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.150

S.I. = ${P_2R_2T_2 - P_1R_1T_1}/100$

150 = ${P × 7.5 × 5 - P × 7.5 × 4}/100$

15000 = 7.5P

P = $15000/{7.5}$

P = $150000/75$ = Rs.2000

Question : 19 [SSC CHSL 2010]

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 ?

a) 5 years

b) 4 years

c) 8 years

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 : 20 [SSC CHSL 2015]

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

a) Rs.70

b) Rs.30

c) Rs.50

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.400

S.I. = ${2400 × 5 × 4}/100$ = Rs.480

Required difference

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

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