Question

Peter lent some amount of money at 5% simple interest and an equal amount of money at 7% simple interest each for 3 years. If total interest earned on both the sum was Rs 360,what amount was lent in each case

Answer 1

The principal amount lent at each case is Rs 1000 .

Step-by-step explanation:

Given as :

The principal amount = Rs p

The rate of interest = r = 5% at simple interest

The time period = t = 3 years

Let The simple interest at 5% = Rs S.I

Let The simple interest at 7% = Rs s.i

Total interest earn = Rs 360

From Simple Interest

S.I = $\dfrac{principal\times rate\times time}{100}$

Or, S.I = $\dfrac{p\times 5\times 3}{100}$

Again

The principal amount = Rs p

The rate of interest = r = 7% at Simple interest

The time period = t = 3 years

Let The Simple interest = Rs s.i

Or, s.i = $\dfrac{principal\times rate\times time}{100}$

Or, s.i = $\dfrac{p\times 7\times 3}{100}$

Now , The Total interest earn from both the case = Rs 360

So, A/Q

Total interest = Interest earn at 5% + interest earn at 7%

Or, Total interest = S.I + s.i

Or, Total interest = $\dfrac{p\times 5\times 3}{100}$  +  $\dfrac{p\times 7\times 3}{100}$

Or, Rs 360 = $\dfrac{p\times 5\times 3}{100}$  +  $\dfrac{p\times 7\times 3}{100}$

Or, Rs 360 × 100 = 15 p + 21 p

Or, 36 p =  360 × 100

∴          p = $\dfrac{36000}{36}$

i.e        p = Rs 1000

So, The principal amount lent at each case = p = Rs 1000

Hence, The principal amount lent at each case is Rs 1000 . Answer