Question

The sum of three numbers is 68 if the ratio of the first and second be 2:3 and the between second and third be5:3 thenwhat is the second number?

Answer 1

Solution ➡

The sum of the 3 numbers = 68

Let the first number be :- x

Let the second number be :- y

Therefore the third number is :- 68 - ( x + y )

x : y = 2 : 3

➡ x = 2y / 3

➡ y = 3x / 2 _________________ ( i )

y : 68 - ( x + y) = 5 : 3

➡ 3y = 340 -5x - 5y

➡ 8y = 340 - 5x

➡ y = ( 340 - 5x ) / 8 _____________ ( ii )

Equating both the equations (as both are equal to y ) i and ii we get ,

3x / 2 = ( 340 - 5x ) / 8

➡ 3x = ( 340 - 5x ) / 4

➡ 12 x = 340 - 5x

➡ 12x + 5x = 340

➡ 17x = 340

➡ x = 20

Therefore, the value of x or the first number is 20

Then the second number will be -

y = 3x / 2

➡ y = ( 3 × 20 ) / 2

➡ y = 60 / 2

➡ y = 30

Therefore the third number will be -

68 - ( 20 + 30 )

= 68 - 50

= 18

$\huge\mathfb{Solution :-}$

First number = 20

Second number = 30

Third number = 18