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

Question : 21 [SSC CGL Prelim 2005]

A sum of Rs.1500 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 years is equal to that on another part at 12.5% per annum for 4 years. The sum lent out at 12.5% is :

a) Rs.1000

b) Rs.500

c) Rs.1250

d) Rs.750

Answer: (d)

Using Rule 1,

Let the sum lent out at 12.5% be x

Sum lent out at 10% = 1500 - x

Now, ${(1500 - x) × 10 × 5}/100$

= ${x × 12.5 × 4}/100$

50 (1500 - x ) = 50x

2x = 1500

$x = 1500/2$ = Rs.750

Question : 22 [SSC CGL Prelim 2004]

Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was Rs. 760, what amount was lent in each case ?

a) Rs.1800

b) Rs.1700

c) Rs.2000

d) Rs.1900

Answer: (c)

Using Rule 1,

Let the sum lent in each case be x.

Then, ${x × 9 × 2}/100 + {x × 10 × 2}/100$ = 760

${x × 2}/100$(9 + 10) = 760

${2 × 19x}/100$ = 760

$x = {760 × 100}/{2 × 19}$ = Rs.2000

Question : 23 [SSC CGL Prelim 2007]

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) 5 years

b) 4 years

c) 8$2/3$ years

d) 6$1/4$ years

Answer: (d)

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

Question : 24 [SSC CPO S.I.2006]

If the simple interest for 6 years be equal to 30% of the principal, it will be equal to the principal after

a) 30 years

b) 20 years

c) 22 years

d) 10 years

Answer: (b)

Let the principal be P and rate of interest be r %

According to the question,

${30P}/100 = {P × R × 6}/100$

30 = 6 R

R = 5

Now, let interest be equal to principal in T years.

P = ${P × 5 × T}/100$

T = $100/5$ = 20 years.

Using Rule 5,

Here, n = $30/100 = 3/10$, T = 6 years.

RT = n × 100

R × 6 = $3/10$ × 100

R = 5%

As,S.I. = P

S.I. = ${P × R × T}/100$

100 = RT

100 = 5 × T

This is possible only when T = 20.

Question : 25 [SSC CHSL 2012]

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) 0.25%

b) 0.10%

c) 1.00%

d) 0.50%

Answer: (a)

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

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