Question

The sum of three numbers is 98. if the ratio between first and second be 2:3.and that between second and third be 5:8 the find the second number

Answer 1

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Method 1 :-

The numbers are x, y, and z.

Given, $x + y + z = 98$

So, $\frac{x}{y} = \frac{2}{3}$
And, $\frac{y}{z} = \frac{5}{8}$

Isolating x and z in these equations :

We have, $x = \frac{2y}{3}$

And, $\frac{8y}{5}= z$

Expressing the sum in terms of y :

So, $\frac{2y}{3} + y + \frac{8y}{5} = 98$

Removing the fractional denominators : 

⇒ $10y + 15y + 24y = 98 \times 15$

⇒ $49y = 98 \times 15$

Thus, y = 30

From there, x = 20, and z = 48.

Method 2 :-

Let, $x + y + z = 98$

So, $x : y= 2 : 3$

And, $y : z= 5 : 8$

Now, Since both ratios consider y, write x : y: z as one ratio around y’s LCM of 15 :

⇒ $x : y = 10 : 15$

⇒ $y : z = 15 : 24$

Thus, $x : y : z = 10 : 15 : 24$

Here, $10 + 15 + 24 = 49$ “parts”,
But we know, $x + y + z = 98$ 

So, doubling each value, we get :

$x : y : z= 20 : 30 : 48$

Method 3 :-

Let the three parts be A , B and C.

Then,
A : B = 2 : 3 and B : C = 5 : 8

--Further Calculations regarding this method in attached image--

∴ The 2nd Number is 30.

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Regards

#ExoticExplorer

Answer 2

Answer:

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.