Question

24
What is the sum (in Rs) which when divided among A.B.C.D in the proportion 2:3:5:8 provides rs 8420
less to D than what it provides to him when the proportion is
1/2,1/3,1/5,1/8​

Answer 1

Given:

Sum divided among A, B, C, D in proportion $2:3:5:8$

To find:

To find out the total sum divided among individuals.

Explanation:

• Here we will simply assume the total sum of money divided to be "x".
• We will calculate the proportion given to D and then calculate "x".

Solution:

Let the total sum of money "x"

Now the old proportion of D:

$\frac{8}{2+3+5+8} = x\\\\\frac{8}{18} = x\\\\= \frac{4x}{9}$

The New proportion of D:

first, we will take the LCM

LCM of $2, 3, 5, 8 = 120$

$60: 40:24:15$

$\frac{15}{60+40+24+15} =x \\\\\frac{15}{139} = x\\\\=\frac{15x}{139}$

Total sum:

$\frac{4x}{9} - \frac{15x}{139} = 8420\\\\\frac{139 *4x - 9*15x}{1251} = 8420\\\\\frac{556x - 135x}{1251} = 8420\\\\421x = 8420 *1251\\\\x = 20*1251\\\\x = 25020$

Hence, the total sum divided among them is $25020$