Question

1. The difference between the simple interest for 3 years and 5 years on Rs. 20000 is
Rs. 2000. What is the Rate of interest ?
1) 5 %
2) 10 %
3) 7.5 %
4) 4 %.​

Answer 1

Given :

Difference between the Simple interest for 3 years and 5 years on Rs. 20000 is Rs. 2000

so,

• Principal Money, P = Rs. 20000
• t₁ = 3 yrs ; t₂ = 5 yrs
• Difference between the Simple interest yielded for 3 yrs and 5 yrs = Rs. 2000

To find :

• Rate of Interest, R =?

Knowledge required :

• Formula to calculate Simple Interest (S.I)

$\red{\bigstar}\boxed{\sf{S.I.=\dfrac{P\times R\times t }{100}}}$

[Where S.I. is the Simple interest on a Principal sum P, with Rate of interest R and time period t]

Solution :

Using Formula for Simple interest and Given Information

$\implies\sf{S.I.\:for\:5\;yrs - S.I.\;for\;3\;yrs= 2000}$

$\implies\sf{\dfrac{P\times R\times t_2}{100}-\dfrac{P \times R\times t_1}{100}= 2000}$

$\implies\sf{\dfrac{P\times R\times t_2-(P\times R\times t_1)}{100}= 2000}$

$\implies\sf{\dfrac{P\times R( t_2-t_1)}{100}= 2000}$

$\implies\sf{P\times R( t_2-t_1)= 2000\times 100}$

$\implies\sf{20000\times R( 5-3)= 200000}$

$\implies\sf{20000\times 2 R = 200000}$

$\implies\sf {2 R = \dfrac{200000}{20000}}$

$\implies\sf {2 R = 10}$

$\implies\sf {R = \dfrac{10}{2}}$

$\implies\underline{\underline{\boxed{\large{\red{\sf{R = 5\;\;\%}}}}}}$

Therefore,

• Rate of Interest will be 5 % per Annum.

Hence,

OPTION (1) 5 % is correct.

Answer 2

Answer:

★ Question :

At what rate will the simple interest on 20000 for 4 years will be equal to the simple interest on 30000 for 3 years at 10%

★ Solution : :

⋆ In 1st case :

Principal, P = Rs.20000

Time, T = 4yrs

Rate, R = ?

In second case

⋆ In 2nd case :

Principal, P = Rs.30000

Time, T = 3yrs

Rate, R = 10%

⋆ According to the given condition,

' The simple interest on 20000 for 4 years will be equal to the simple interest on 30000 for 3 years at 10%. '

Since , Simple interest , S.I = PTR/100

⇒ 20000 × R × 4/100 = 30000 × 10 × 3/100

⇒ 200 ×R × 4 = 300 × 10 × 3

⇒800R = 9000

⇒R = 9000/800

⇒R = 90/8

⇒R = 11.25 %

⋆ Hence, the required rate is 11.25 %