Question

At the same rate of simple interest in percent per annum, if a principal becomes the amount of Rs. 7100 in 7 yrs. and of Rs. 6200 in 4 yrs. Let us determine the principal and rate of simple interest in percent per annum.

(Answer : P = Rs. 5000, R = 6%)

Answer 1

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⇒ Let P be the Principal

⇒ Let I be the Interest

⇒ Let R be the rate

⇒ Let T be the time .

⇒ Let A be the amount .

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First case :

A = Rs. 7100

T = 7 y

A = P + I

But I = P R T / 100

➡A = P + P R T / 100

Put the values :

➡7100 = P + P × R × 7 / 100

➡710000 = 100 P + 7 PR

➡P ( 100 + 7 R ) = 7,10,000

➡P = 7,10,000 / ( 100 + 7 R ) ........................( 1 )

Second case :

A = Rs 6200

T = 4 y

A = P + I

➡A = P + P R T / 100

➡6200 = P + P R × 4 / 100

➡6,20,000 = 100 P + 4 P R

➡P ( 100 + 4 R ) = 6,20,000

➡P = 6,20,000 / ( 100 + 4 R ) ..........................( 2 )

Solving ( 1 ) & ( 2 ) :

➡6,20,000 / ( 100 + 4 R ) = 7,10,000 / ( 100 + 7 R )

Cancel 10,000 both sides :

➡62 / ( 100 + 4 R ) = 71 / ( 100 + 7 R )

➡62 ( 100 + 7 R ) = 71 ( 100 + 4 R )

➡6200 + 434 R = 7100 + 284 R

➡434 R - 284 R = 7100 - 6200

➡150 R = 9,00

➡R = 900 / 150

➡R = 6

The rate of interest is 6 %

From ( 2 ) we have :

➡P = 6,20,000 / ( 100 + 4 R )

➡P = 6,20,000 / ( 100 + 4 × 6 )

➡P = 6,20,000 / ( 100 + 24 )

➡P = 6,20,000 / 124

➡P = 5,000

The Principal is Rs . 5,000

$\huge{\mathsf{\underline{ANSWER}}}$

Rate of interest is 6 %

Principal is Rs. 5,000

Hope it helps you (:-))

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Answer 2

A = Rs. 7100

T = 7 y

A = P + I

But I = P R T / 100

A = P + P R T / 100


Putting the values :

7100 = P + P × R × 7 / 100


710000 = 100 P + 7 PR


P ( 100 + 7 R ) = 7,10,000


P = 7,10,000 / ( 100 + 7 R ) eqn.1


Second case :

A = Rs 6200

T = 4 y

A = P + I

A = P + P R T / 100

6200 = P + P R × 4 / 100

6,20,000 = 100 P + 4 P R

P ( 100 + 4 R ) = 6,20,000

P = 6,20,000 / ( 100 + 4 R ) eqn 2


Solving ( 1 ) & ( 2 ) :


6,20,000 / ( 100 + 4 R ) = 7,10,000 / ( 100 + 7 R )

Cancel 10,000 both sides :

62 / ( 100 + 4 R ) = 71 / ( 100 + 7 R )

62 ( 100 + 7 R ) = 71 ( 100 + 4 R )

6200 + 434 R = 7100 + 284 R

434 R - 284 R = 7100 - 6200

150 R = 9,00

R = 900 / 150

R = 6


The rate of interest is 6 %


From ( 2 ) we have :

P = 6,20,000 / ( 100 + 4 R )

P = 6,20,000 / ( 100 + 4 × 6 )

P = 6,20,000 / ( 100 + 24 )

P = 6,20,000 / 124

P = 5,000


The Principal is Rs . 5,000





Rate of interest is 6 %

Principal is Rs. 5,000


Hope it helps you ❤️❤️