Question

The sum of three numbers is 98. If the ratio of the first to second is 2:3 and that of the second to the third is 5:8, then the second number is : ?
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Answer 1

Answer:

30

Step-by-step explanation:

Let the three numbers be x, y and z.

Sum of the numbers is 98.

x + y + z = 98………………(i)

The ratio of the first to the second is 2/3.

x/y = 2/3.

x = 2/3 × y.

x = 2y/3.

The ratio of the second to the third is 5/8.

y/z = 5/8.

z/y = 8/5.

z = 8/5 × y.

z = 8y/5.

Put the value of x = 2y/3 and z = 8y/5 in (i).

2y/3 + y + 8y/5 = 98

49y/15 = 98.

49y = 98 × 15.

49y = 1470.

y = 1470/49.

y = 30 .

Therefore, the second number is 30.

Answer 2

Given:-

• $\sf{Sum\:of\:three\:numbers = 98}$
• $\sf{Ratio\:of\:first\:number\:to\:second\:number = 2:3}$
• $\sf{Ratio\:of\:second\:number\:to\:three\:number}$

To find:-

The second number.

Assumption:-

• $\sf{Let\:the\:first\:number\:be\:x}$
• $\sf{Let\:the\:second\:number\:be\:y}$
• $\sf{Let\:the\:third\:number\:z}$

Solution:-

ATQ,

$\sf{x + y + z = 98 --------->(i)}$

1st case,

$\sf{Ratio\:of\:first\:two\:numbers = 2:3}$

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

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

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

=> $\sf{x = \dfrac{2y}{3}--------->(ii)}$

2nd case

$\sf{Ratio\:of\:second\:number\:to\:third\:number = 5:8}$

= $\sf{y:z = 5:8}$

= $\sf{\dfrac{y}{z} = \dfrac{5}{8}}$

= $\sf{8y = 5z}$

=> $\sf{z = \dfrac{8y}{5}---------->(iii)}$

Now, Substituting the values of x and z in equation (i)

$\sf{x+y+z = 98}$

= $\sf{\dfrac{2y}{3} + y + \dfrac{8y}{5} = 98}$

= $\sf{\dfrac{10y + 15y + 24y}{15} = 98}$

= $\sf{49y = 98\times15}$

= $\sf{y = \dfrac{98\times15}{49}}$

= $\sf{y = 2\times 15}$

= $\sf{y = 30}$

$\sf{\therefore The\:second\:number\:is\:30}$

Putting The value of y in equation (ii)

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

= $\sf{x = \dfrac{2\times30}{3}}$

= $\sf{x = 2\times10}$

= $\sf{x = 20}$

Putting the value of x and y and equation (i)

$\sf{x+y+z = 98}$

= $\sf{20 + 30 + z = 98}$

=> $\sf{50+z = 98}$

=> $\sf{ z = 98-52}$

=> $\sf{z = 46}$

Therefore the three numbers are:-

1st number = x = 20

2nd number = y = 30

3rd number = z = 46