Question

the simple intrest on the certain sum for 4 year at 9% annum is 114rs more than the simple intrest on the same sum of 3year at 10% per annum find sum​

Answer 1

Let :

• Sum (or Principal) = P
• SI{1} = I (for 1st case, when t = 4year)
• SI = I' (for 2nd case , when t = 3year)

Given :

• SI{1} = ₹114 + SI{2}
• r = 9% p.a.
• t = 4 years
• r' = 10% p.a.
• t' = 3 years

To find :

Sum or Principal

Formula used :

Interest = P×r×t

Solution :

SI{1} = P × r × t

I = P × (9/100) × 4

I = P × (36/100)

I = 0.36P ....... equation 1

SI{2} = P × r' × t'

I' = P × (10/100) × 3

I' = 0.3P ........equation 2

As SI{1} = ₹114+ SI{2}

=> I = 114 + I'

=> I' = I - 114

putting value of I' in equation 2 , we get;

I - 114 = 0.03P ......equation 3

putting value of I from equation 1 to equation 3 , we get;

$\sf \implies \: (0.36P) - 114 = 0.3P \\ \sf \implies \:0.36P \: - \: 0.3P \: = 114 \\ \sf \implies \:0.06P \: = 114 \\ \sf \implies \:P \: = \dfrac{114}{0.06} \\ \\ \sf \implies \bold{\:P \: = 1900}$

ANSWER :

Sum (or Principal ) = P = ₹1900