TNPSC APTITUDE AND REASONING-SIMPLE INTEREST

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www.tnpsc.academy TNPSC Exams APTITUDE AND REASONING – for Group 1, Group 2, Group 2A, Group 3, Group 4, VAO and Others.

TOPIC: SIMPLE INTEREST

FORMULAE:

i. SI = (P * N * R)/100

Where,
  SI – Simple Interest
  P – Principal
  R – Rate percent per annum
  N – Number of years
  A – Amount

ii. Amount (A) – Principal (P) + Interest (SI)

iii. Principal (P) – (100 * A) / (100 + RT)

iv. (ART) / (100 + RT)

EXAMPLE PROBLEMS

EXAMPLE 1:

In what time 1200 will become 1450. When annual rate of interest is 20%?

Solution:

P (Principle) = 1200, A (Amount) = 1450, R (Rate of Interest) =20%
A = P + SI
1450 = 1200 + SI
SI = 1450 – 1200
SI = 250
SI = (PRT) / 100
250 = (1200* 20 * T) / 100
250 = 240T
T= 25 / 24

Answer => T = 1 (1 /24) yrs

EXAMPLE 2 :

A Sum at simple interest of 4% per annum amounts to 3120 in 5 yrs. Find the sum?

Solution :

T (No. of Years) = 5 yrs, R (Rate of Interest) = 4%, A (Amount) = 3120
Method 1 :
P= (100 * A) / (100 + RT)
= (100 * 3120) / (100 + 4 * 5)
= (100 * 3120) / 120

Answer => P = 2600

Method 2:

SI = PRT / 100
= (P * 4 * 5) / 100
SI = P / 5
Amount = P + SI
= P + (P / 5) = 6P / 5
According to the question,
Amount = 3120 = 6P / 5 = 3120
P = (3120 * 5) / 6 = 2600

Answer => P = 2600

Note 1 :
If a sum of money becomes n times in T yr at simple interest, then formula for calculating rate of interest will be given as
                         R = [ 100 (n – 1)] / T %

Example :

A sum of money becomes 4 times in 20 yrs at simple interest. Find the rate of interest?

Solution :

T (No. of Years) = 20 yrs, n = 4
R = [100 (n – 1) / T]
= [100 (4 – 1) / 20]
= (100 * 3) / 20

Answer => R = 15 %

Note 2 :
If a sum of money at a certain rate of interest becomes “n” times in T1 yr and “m” times in T2 yr, then formula for T2 will be given as
                                T2 = [(m – 1) / (n – 1)] * T1

Example :

If a sum of money at simple interest becomes 4 times of itself in 15 yrs, it will become 3 times in,

Solution :

T1 = 15 yrs, n = 4, m = 3,

T2 = [(m -1) / (n – 1)] * T1
= [(3 – 1) / (4 – 1)] * 15
= (2 / 3) * 15

Answer => T2 = 10 yrs

Note 3 :
If a sum of money in a certain time becomes “n” times at R1 rate of interest and “m” times at R2 rate of interest, then formula for R2 will be given as,

                                  R2 = [(m – 1) / (n – 1)] * R1

Example :

In a certain time, a sum becomes 3 times at the rate of 5 % per annum. At what rate of interest, the sum becomes 6 times in same duration?

Solution :

n = 3, m = 6, R1 = 5%, R2 = ?
R2 = [(m – 1) / (n – 1)] * R1
= [(6 – 1) / (3 – 1)] * 5
= [5 / 2] * 5
= 25 / 2

Answer => R2 = 12.5 %

[/vc_column_text][/vc_column][/vc_row][vc_row][vc_column][vc_custom_heading text=”Exercise Problems for Practice ” font_container=”tag:h4|text_align:left” google_fonts=”font_family:Arvo%3Aregular%2Citalic%2C700%2C700italic|font_style:400%20regular%3A400%3Anormal”][vc_column_text]1 ) In what time, does a sum of money become fourfold at the simple interest rate of 10 % per annum?

a) 10 years                 b) 20 years                   c) 30 years                   d) 40 years

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N = 4, R = 10 %

R = [100 * (n – 1)] / T

10 = [100 * (4 – 1)] / T

10 = [100 * 3] / T

T = 30 yrs

Answer => c) 30 years

[/vc_toggle][vc_column_text]2 ) A certain sum becomes 3 fold at 4 % annual rate of interest. At what rate, it will become 6 fold?

a) 10 %                      b) 12 %                    c) 15 %                        d) 20 %

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M = 6, n = 3, R1 = 4

R2 = [(m – 1) / (n – 1)] * R1

= [(6 – 1) / (3 – 1)] * 4

= [5 / 2] * 4

  R2 = 10 %

Answer => a) 10 %

[/vc_toggle][vc_column_text]3 ) A sum of 2668 amounts to 4669 in 5 yrs at the rate of simple interest. Find the rate percent

a) 10 %                  b) 12 %              c) 15 %                        d) 20 %

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N = 5, P = 2668, A = 4669

SI = A – P

= 4669 – 2668 = 2001

SI = 2001

SI = PNR / 100

2001 = (2668 * 5 * R) / 100

R = 15 %

  Answer => c) 15%

[/vc_toggle][vc_column_text]4 ) Find the difference in amount and principal for ₹ 4000 at the rate of 5 % amount interest in 4 yr?

a) 780             b) 800                          c) 810              d) 820

[/vc_column_text][vc_toggle title=”Solution” custom_font_container=”tag:h2|font_size:17|text_align:left|color:%23dd5858″ custom_google_fonts=”font_family:Vollkorn%3Aregular%2Citalic%2C700%2C700italic|font_style:400%20regular%3A400%3Anormal” el_id=”1476331757239-642fda39-e8e6″ use_custom_heading=”true”]

R = 5 %, N = 4, P = 4000

SI = PNR / 100

= (4000 * 5 * 4) / 100

SI = 800

A = SI + P

= 800 + 4000

A = 4800

Difference in amount and principal,

SI = A – P => 4800 – 4000

SI = 800

                     Answer =>  b) 800

[/vc_toggle][vc_column_text]5 ) A sum of money triple itself at SI in 12 yrs. In how many years will it become 9 times?

a) 36 years             b) 40 years                               c) 42 years                   d) 48 years

[/vc_column_text][vc_toggle title=”Solution” custom_font_container=”tag:h2|font_size:17|text_align:left|color:%23dd5858″ custom_google_fonts=”font_family:Vollkorn%3Aregular%2Citalic%2C700%2C700italic|font_style:400%20regular%3A400%3Anormal” el_id=”1476331832030-1d467c18-1ced” use_custom_heading=”true”]

M = 9, n = 3, T1 = 12

T2 = [(m – 1) / (n – 1)] * T1

= [8 / 2] * 12

T2 = 48 yrs

           Answer =>  d) 48 years

[/vc_toggle][vc_column_text]6 ) Amit takes some loan from Akash for 2 yr at the rate of 5 % per annum and after 2 yr he gave back ₹ 6600 to Akash and completed the payment of    his loan. Find the interest paid by Amit?

a) 330             b) 450                          c) 600                          d) 820

[/vc_column_text][vc_toggle title=”Solution” custom_font_container=”tag:h2|font_size:17|text_align:left|color:%23dd5858″ custom_google_fonts=”font_family:Vollkorn%3Aregular%2Citalic%2C700%2C700italic|font_style:400%20regular%3A400%3Anormal” el_id=”1476331905809-38a3a1da-e513″ use_custom_heading=”true”]

T = 2 yr, R = 5%, A = 6600

SI = ART / (100 + RT)

SI = (6600 * 5 * 2) / (100 + 5 * 2)

= (6600 * 10) / 110

SI = 600

      Answer =>  c) 600

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