Question

a sum of money amounts to rs 1500 in 5 years. find the principal and rate of interest if interest is 1/3 of principal​

Answer 1

Step-by-step explanation:

A= 1500

t= 5yrs

si= 1/3 of p

si = 1500/3

= 500

p= 1500 -500

=1000

r= si × 100/ p × t

= 500×100/ 1000× 5

= 50/5

= 10%

Answer 2

Given: Time= 5 years

           Amount= ₹ 1500

           Interest= $\frac{1}{3}$ of Principal

To Find: i) Principal

             ii) Rate of Interest

Solution:

Amount(A) = Principal(P) + Simple Interest(S.I)

⇒ 1500= P + S.I

We know, S.I = $\frac{1}{3}$ of P

⇒ 1500= P + $\frac{1}{3}$P

           $=\frac{3P+P}{3}$

⇒ 1500 $\times$ 3= 3P + P

⇒ 4500= 4P

⇒ P = $\frac{4500}{4}$

⇒ P =  ₹ 1125

According to question,

S.I = $\frac{1}{3}$ of Principal

    = $\frac{1}{3}$ of 1125

    = $\frac{1}{3}\times 1125$

    = ₹ 375

Simple Interest (S.I)$=\frac{Principal (P)\times Time(T)\times Rate of Interest(R)}{100}$

⇒ 375= $\frac{1125\times5\times R}{100}$

⇒ 375 $\times$ 100= 5625 $\times$ R

⇒ R= $\frac{37500}{5625}$

⇒ R= 6.67%

Answer: The principal is ₹ 1125 and the rate of interest is 6.67%.