Question

a person invested a sum of money for 5years at the rate of 6% per annum simple interest. after 5 years, he re invested the same principal for 6 years at the rate of 8% per annum simple interest. If the total interest earned from both these investments is Rs.12480, find the sum invested by him​

Answer 1

Let :-

• The sum invested by him be P

To Find :-

• The Sum invested by him = ?

Solution :-

To calculate the sum invested by him at first we have to find out si for 5 years and 6 years then set up equation. By solving equation We can easily calculate the sum invested by him.

Calculation for Case - (i) :-

• Principal = P. Rate = 6%. Time = 5 years

⟶ SI = P × T × R/100

⟶ SI = P × 5 × 6/100

⟶ SI = 30P/100------(i)

Calculation for Case - (ii) :-

• Principal = P. Rate = 8%. Time = 6 years

⟶ SI = P × T × R/100

⟶ SI = P × 6 × 8/100

⟶ SI = 48P/100--------(ii)

Calculation for Principal :-

• Total interest = Rs. 12480.

⟶ SI for Case - (i) + SI for Case - (ii) = 12480

⟶ 30P/100 + 48P/100 = 12480

⟶ (30P + 48P)/100 = 12480

⟶ 78P/100 = 12480

⟶ 78P = 12480 × 100

⟶ P = 160 × 100

⟶ P = 16000

Hence,

• The sum invested by him = Rs. 16000

Answer 2

G I V E N :

A person invested a sum of money for 5years at the rate of 6% per annum simple interest. after 5 years, he re invested the same principal for 6 years at the rate of 8% per annum simple interest. If the total interest earned from both these investments is Rs.12480, find the sum invested by him.

S O L U T I O N :

Case I

According to the question we are given with several datas. They are

Let the principal be P

Time (T) = 5 years

Rate (R) = 6 % p.a

Now, to get the simple interest we need to apply

$\sf{S.I. = \frac{P × R × T}{100}}$

$\sf{S.I. = \frac{P × 6 × 5}{100}}$

$\sf{S.I. = \frac{30P}{100}}$

$\star \: \underline{ \boxed{\sf{ \pink{S.I. = \frac{3P}{10}} }}}$

For case 1 we got the simple interest as 3P/10

Case II

Now, here also we are loaded with the new datas. Noting them down

The pricipal is P1

Time (T1) = 6 years

Rate (R1) = 8 % p.a

Now, getting the simple interest for case II

$\sf{S.I. = \frac{P_{1} × R_{1} × T_{1}}{100}}$

$\sf{S.I. = \frac{P× 8×6}{100}}$

$\sf{S.I. = \frac{48P}{100}}$

$\star \: \underline{ \boxed{ \sf{ \red{S.I. = \frac{12P}{25}} }}}$

For case II the interest is 12P/25

Now, adding both these cases which equals the total interest earned

Case I + Case II = Total Interest earned

$\rightharpoonup \sf{ \frac{3P}{10} + \frac{12P}{25} = 12480 }$

Now, getting the L.C.M. The L.C.M of 10, 25 is 50

$\rightharpoondown\sf{ \frac{3P ( 5)}{10 ( 5)} + \frac{12P(2)}{25(2)} = 12480 }$

$\rightharpoonup \sf \frac{15P}{50} + \frac{24P}{50} = 12480$

$\rightharpoondown \sf \frac{39P}{50} = 12480$

$\rightharpoonup \sf39P = 12480(50)$

$\rightharpoondown \sf39P = 624000$

$\rightharpoonup \sf P = \frac{624000}{39}$

$\star \: \: \boxed{ \green{\frak{ {\sf P} = 16000}}}$

• Hence, the sum invested is ₹ 16000