Question

the ratio of 2 number is 2:5 their difference is 390.find the longest number
a)250 b)350 c)650 d)550​

Answer 1

Given :

• The ratio of two numbers is 2:5 .
• Difference is 390 .

To Find :

• Larger number .

Solution :

$\longmapsto\tt{Let\:first\:number\:be=2x}$

$\longmapsto\tt{Let\:second\:number\:be=5x}$

A.T.Q :

$\longmapsto\tt{5x-2x=390}$

$\longmapsto\tt{3x=390}$

$\longmapsto\tt{x=\cancel\dfrac{390}{3}}$

$\longmapsto\tt{x=130}$

$\purple\longmapsto\:\large\underline{\boxed{\bf\blue{x}\pink{=}\red{130}}}$

Therefore :

$\longmapsto\tt{First\:Number=2(130)}$

$\longmapsto\tt\bf{260}$

$\longmapsto\tt{Second\:Number=5(130)}$

$\longmapsto\tt\bf{650}$

So , 650 is larger than 260 .

Option c)650 is Correct.

Answer 2

Given :

The Ratio of two numbers is 2:5 . and,

Their Difference is 390.

To Find :

Biggest Number

Solution :

Let the Numbers be 2x and 5x .

so, According to Question

$\rm⇢ \: \: 5x - 2x = 390$

$\rm⇢ \: \: 3x = 390$

$\rm⇢ \: \: x = 130$

Then, The Numbers are :

2x = 2(130) = 260

5x = 5(130) = 650

______________________________

FINAL ANSWER :

Biggest Number is 550.

so, Option (c) is the correct answer.