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

Answer:

second number is 30

Step-by-step explanation:

Let the three numbers be x, y and z.

x+y+z = 68 -------1

x:y=2:3, so

2y = 3x, or

x = (2/3)y -------2

y:z::5:3, or

3y = 5z, or

z = (3/5)y -------3

Put the values of x from (2) and z from (3) in (1) to get

(2/3)y + y +(3/5)y = 68 …(4)

The LCM of 3 and 5 is 15. Hence (4) becomes

10y + 15y + 9y = 68*15, or

34y = 68*15, or

y = (68/34)*15 = 30.

Hence x = (2/3)y = 20 and z = (3/5)y = 18.

The three numbers are 20, 30 and 18.

Answer 2

Let the three numbers be x , y and z .

A/Q

$\longrightarrow$The sum of three numbers is 68 .

x + y + z = 68 ______(1)

The ratio of First and second number is 2:3 .

$\sf \therefore \dfrac{x}{y} = \dfrac{2}{3}$

3x = 2y

$\sf \implies \: x= \dfrac{2}{3} y$

Also , the ratio of second and third number is 5:3 .

$\sf \therefore \dfrac{y}{z} = \dfrac{5}{3}$

5 z = 3y

$\sf \implies z = \dfrac{3}{5} y$

Substituting value of x and z in equation 1 .

$\sf \: \dfrac{2}{3} y + y + \dfrac{3}{5} y = 68$

$\implies \sf \dfrac{10y + 15y + 9y}{15} = 68$

$\implies \sf \dfrac{34 \: y}{15} = 68$

$\implies \sf \: 34y = 68 \times 15$

$\implies \sf 34y = 1020$

$\implies \sf y = \dfrac{1020}{34}$

$\boxed{ \sf \therefore \blue{y = 30}}$

Hence , the second number is 30 .