Question

94. Simple and compound interest on
principle at a certain rate of interest for 2 years
is Rs 1400 and Rs 1470 respectively. What is
the principal (in Rs)?
A. 8500
B. 7000
C. 6000
D. 6500​

Answer 1

Step-by-step explanation:

s.i =p×r×t

1400=p×2×r

700=pr

compound interest=A=P(1+r/n)^nt

1470=700/r+(1+r/

Answer 2

The principal is Rs. 7000.

Correct option: B. 7000

Step-by-step explanation:

Let, principal = P and rate of interest (simple and compound) = r% p.a.

Step 1.

Given, simple interest for 2 years = Rs. 1400

⇒ $\dfrac{P\times 2\times r}{100}=1400$

⇒ Pr = 70000 ... ... (1)

Step 2.

Given, compound interest for 2 years = Rs. 1470

⇒ $P(1+\dfrac{r}{100})^{2}-P=1470$

⇒ $P(1+\dfrac{2r}{100}+\dfrac{r^{2}}{10000}-1)=1470$

⇒ $P(\dfrac{r}{50}+\dfrac{r^{2}}{10000})=1470$

⇒ $P\times \dfrac{200r+r^{2}}{10000}=1470$

⇒ $P(200r+r^{2})=14700000$ ... ... (2)

Step 3.

From (1) and (2), we get

$\dfrac{70000}{r}\times (200r+r^{2})=14700000$

⇒ 14000000 + 70000r = 14700000

⇒ 70000r = 700000

⇒ r = 10

So, rate of interest (both simple and compound) is 10% p.a.

Step 4.

Putting r = 10 in (1), we get

P × 10 = 70000

$\Rightarrow P=\dfrac{70000}{10}$

⇒ P = 7000

Thus the principal is Rs. 7000.

#SPJ3