Question

Maneela lent Rs. 8000 partly at the rate of 5% and partly at the rate of 6% per annum simple interest. The total interest she get after 2 years is Rs. 820, then in which ratio will Rs. 8000 is to be divided?

A) 7:1 B) 13:5 C) 15:7 D) 2:7

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume that, first part is Rs.x

Than,

→ P = Rs.x

→ Rate = 5% .

→ Time = 2 years.

→ SI = (P * R * T) / 100

→ SI = (x * 5 * 2)/100

→ SI = Rs.(x/10)

Similarly,

→ Rest P = Rs.(8000 - x).

→ Rate = 6% .

→ Time = 2 years.

→ SI = (P * R * T) / 100

→ SI = {(8000-x) * 6 * 2}/100

→ SI = Rs.(8000-x)*12/100

Now, we have given That, The total interest she get after 2 years is Rs. 820.

So,

→ (x/10) + (8000-x)12/100 = 820

→(10x + 8000*12 - 12x) /100 = 820

→ 96000 - 2x = 82000

→ 2x = 96000 - 82000

→ 2x = 14000

→ x = Rs.7000.

Hence,

→ First Part = Rs.7000

→ Second Part = (8000-1000) = Rs.1000

∴ Required Ratio = 7000:1000 = 7:1 (A) (Ans.)

Answer 2

${ { \mathfrak{ \huge{ \underline{ \underline{Solution:-}}}}}}$

${ \bold{ {GIVEN-}}}$

☞ Total sum of money = Rs. 8000

☞ Total interest after 2 years = Rs. 820

☞ Let the first part be Rs. x and the second part be Rs.(8000-x)

❶. First Part....

◆ Principal (P) = Rs. x

◆ Rate ( R ) = 5 %

◆ Time ( T ) = 2 years

✰ Simple interest (S.I.) = ( P*R*T)/100

= ( x * 5 * 2 )/100

= Rs. 10x/100

❷. Second part...

◆ Principal (P) = Rs.(8000-x)

◆ Rate (R) = 6%

◆ Time ( T ) = 2 years

✰ Simple interest ( S.I.) = ( P*R*T)/100

= {(8000-x) * 6 * 2} /100

= Rs. 12(8000-x)/100

❋ S.I. on 1 + S.I. on 2 = Rs. 820

${ \bold{ \frac{10x}{100} + \frac{12(8000 - x)}{100} = 820}}$

${ \bold{ \implies{ \frac{10x + 12(8000 - x)}{100} = 820}}}$

${ \bold{ \implies{10x + 96000 - 12x = 82000}}}$

${ \bold{ \implies{12x - 10x = 96000 - 82000}}}$

${ \bold{ \implies{2x = 14000}}}$

${ \bold{ \implies{x = Rs. \: 7000}}}$

therefore,.

✪. first part = Rs. x = Rs. 7000

✪. Second part = Rs.(8000-x) = Rs.(8000-7000) = Rs.1000

☞ hence, the ratio in which Rs. 8000 is divided ....

7000/1000 = 7 : 1