Question

divide rs.8000 into two parts such that if one part were lent at 7½% per annum for two years and the other at 8% per annum for three years the total interest received is rupees 1416​

Answer 1

Rs 5600 & Rs 2400 are two parts if Rs.8000 is divided in two parts such that one part be lent at 15/2℅ p.a. for 2years and the other at 8℅ p.a. for 3 Years and total interest = Rs 1416

Step-by-step explanation:

Let say first Part = Rs P

then second Part = 8000 - P Rs

First Part interest

P = P

R = 15/2 %

T = 2 Years

SI = P * (15/2) * 2 /100 = 15P/100 Rs

Second Part interest

P = 8000 - P

R = 8%

T = 3 Years

SI = (8000 - P) * 8 * 3 /100 = 1920 - 24P/100 Rs

15P/100 + 1920 - 24P/100 = 1416

=> 504 = 9P/100

=> 56 = P/100

=> P = 5600

1st Part = Rs 5600

2nd Part = 8000 - 5600 = 2400 Rs

Answer 2

Correct question is "Divide rs.8000 into two parts such that if one part were lent at 7½% per annum for two years and the other at 8% per annum for three years the total interest received is rupees 1416.Find amount of two parts ? "

Answer:

Required first part is 5600 rupees and second part is 2400 rupees.

Step-by-step explanation:

Given,divide rs.8000 into two parts.

Let first part is x rupees and second part is (8000-x) rupees.

It is also given that one part were lent at 7½% per annum for two years and the other at 8% per annum for three years.

Let x part lent at $7 \frac{1}{2} \%$ per annum for 2 years and (8000-x) part at 8% per annum for three years.

We know,

Simple interest $= \frac{prt}{100}$

Where p is principal,r is rate of interest and t is time.

When,

$p = x \: rupees \\ r = 7 \frac{1}{2} \% = \frac{15}{2} \% \\ t = 2 \: years$

Simple interest

$= \frac{x \times \frac{15}{2} \times 2 }{100} \\ = \frac{3x}{20}$

and when,

$p =(8000 - x) \: rupees \\ r = 8\% \\ t = 3 \: years$

Simple interest

$= \frac{(8000 - x) \times 8 \times 3}{100} \\ = \frac{(8000 - x) \times 6}{25}$

According to question,

$\frac{3x}{20} + \frac{(8000 - x) \times 6}{25} = 1416 \\ \frac{15x + 192000 - 24x}{100} = 1416 \\ \frac{192000 - 9x}{100} = 1416 \\ 192000 - 9x = 141600 \\ 9x = 192000 - 141600 \\ 9x= 50400 \\ x = \frac{50400}{9} \\ x = 5600$

So, required first part is 5600 rupees and second part is (8000-5600) = 2400 rupees.

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