Question

a certain sum of money lent out at simple interest amounts to Rs 1550 in 3 years and Rs 1750 in 5 years find the principal and the rate of interest

Answer 1

1550 in 3years
1750 in 5 years

so
interest of 2 years is 1750-1550= 200

interest of 1 years ...............= 200/2=100
................3 years ................= 100×3= 300

so
sum = 1550 - 300= 1250

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we have sum =1250 interest =100 time= 1 year

Rate = (interest×100)/ (sum × time)
R====(100×100)/ (1250×1)

R= 10000/1250
R= 8

$sum = 1250 \\ rate = 8\%$

Answer 2

The principal is Rs.1250 and rate of interest is 8%

Step-by-step explanation:

Case 1 :

Principal = P

rate of interest = R

Amount = 1550

Simple interest = 1550-P

Time = 3 years

$SI = \frac{P \times T \times R}{100} \\1550-P=\frac{P \times 3 \times R}{100}$

$\frac{100(1550-P)}{3P}=R -----1$

Case 2:

Principal = P

rate of interest = R

Amount = 1750

Simple interest = 1750-P

Time = 5 years

$SI = \frac{P \times T \times R}{100}\\1750-P=\frac{P \times 5 \times R}{100}$

$\frac{100(1750-P)}{5P}=R ---2$

Equate 1 and 2

$\frac{100(1550-P)}{3P}=\frac{100(1750-P)}{5P}$

P =1250

Substitute the value in 1

$\frac{100(1550-1250)}{3(1250)}=R \\8\% = R$

Hence The principal is Rs.1250 and rate of interest is 8%

#Learn more:

A sum of money lent out at simple interest amounts to Rs 2295 in 3 year and Rs 3009 in 5 year. Find the principal.

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