Question

Divide rs.414 into three parts such that first one is 2/3 of the second and the ratio between second and third is 5:7

Answer 1

Let the second one is x
First one is 2x/3
Let the thrid one is z
X:z=5:7
7x=5z
2x /3+x+7x/5=(10x+15x+21x)/15=46x/15=414
X=135
The three parts are 90,135,189

Answer 2

The three numbers are 135 , 90 and 189.

• Let the second number be x.

• First number will be 2/3x.

• Now ratio of second and third is 5:7.

• Let the third number be z.

Now x : z = 5 : 7.

z = 7x/5.            (Equation 1)

• Now sum of all the three is 414.

x + 2/3x + z = 414

x + 2/3x + 7/5x = 414            (From equation 1)

$\frac{15x + 10x + 21x }{15}$ = 414

$\frac{46x}{15}$ = 414

x = 135

• Now second number is 2/3x = 90

• Third number is 7/5x = 189