Question

A sum of Rs. 72,400 is lent into three parts. The first part is lent for 4 years at the rate of 10%pa, the second part is lent for 6 years at the rate of 9%pa, and the third part is lent for 4 years at the rate of 17%pa. Find the second part if interests are same in all three cases? *

Answer 1

Answer:

22000

Step-by-step explanation:

Answer 2

Given that,

The first part is lent for 4 years at the rate of 10% pa.

The second part is lent for 6 years at the rate of 9% pa.

The third part is lent for 4 years at the rate of 17% pa.

The sum of Rs 72400.

Let the three parts be Rs x, Rs y and Rs z.

According to question,

$\dfrac{x\times4\times10}{100}=\dfrac{y\times9\times6}{100}=\dfrac{z\times17\times4}{100}$

$\dfrac{x40}{100}=\dfrac{y54}{100}=\dfrac{68z}{100}=k$

$x=\dfrac{100k}{40}$...(I)

$y=\dfrac{100k}{54}$....(II)

$z=\dfrac{100k}{68}$....(III)

We need to calculate the value of k

Using given data

$x+y+z=72400$

$\dfrac{100k}{40}+\dfrac{100k}{54}+\dfrac{100k}{68}=72400$

$2.5k+1.85k+1.47k=72400$

$5.82k=72400$

$k=\dfrac{72400}{5.82}$

$k=12439.86$

We need to calculate the amount of second part

Using second equation

$y=\dfrac{100k}{68}$

Put the value of k

$y=\dfrac{100\times12439.86}{68}$

$y=18293.91$

Hence, The amount of second part is Rs. 18293.91