Question

8.
The ratio between two numbers is 5:9, and their
difference is 188, then what is the sum of the
two numbers ?
(A) 788 (B) 658 (C) 508 (D) 888​

Answer 1

$\huge\mathbb{SOLUTION:-}$

• let the number be x

• 5x and 9x

• Their difference= 188

$\bf\underline{\red{\:\:\:\:\:\:\:\:A.T.Q:-\:\:\:\:\:\:\:}}$

$\sf\implies 9x-5x=188\\ \\ \sf\implies 4x=188\\ \\ \sf\implies x=\cancel{\dfrac{188}{4}}\\ \\ \sf\implies x=47$

Now the number's

$\sf\bullet 9x = 9\times 47\\ \sf\implies 423\\ \\ \sf\bullet 5x= 5\times 47\\ \sf\implies 235$

Now the sum of numbers

$\sf\implies 423+235\\ \\ \sf\implies 658$

$\boxed{\sf{\purple{Their \:Sum\:=658\:(option\:B)}}}$

Answer 2

Answer:

$\blue{\underline{\red{\boxed{\text\purple{Sum \: of \: numbers = 658 }}}}}$

Question:-

The ratio between two numbers is 5:9 ,their difference is 188,then what is the sum of the two numbers?

A) 788 B)658 C)508 D)888

Solution:-

Given:-

• Ratio between two numbers = 5 : 9
• Difference = 188

To find:-

• Sum of two numbers = ?

Let the two numbers be 5y and 9y respectively.

A/Q,

$\Rightarrow\rm 9y - 5y = 188 \\\\\Rightarrow\rm 4y = 188 \\\\\Rightarrow\rm y = 188/4 \\\\\Rightarrow\rm y ={\boxed{\rm{47}}}$

$\rm Now,\\\\\rm 1st \: number = 5y \\\\\Rightarrow\rm 1st \: number = 5(47) \\\\\Rightarrow\rm 1st \: number = {\boxed{\rm{235}}}$

$\rm Again, \\\\\rm 2nd \: number = 9y \\\\\Rightarrow\rm 2nd \: number = 9(47) \\\\\Rightarrow\rm 2nd\: number ={\boxed{\rm{423}}}$

$\rule{200}{1}$

$\Rightarrow\rm Sum \: of \:numbers = 1st \: number + 2nd \: number \\\\\Rightarrow\rm Sum \: of \: numbers = 235 + 423 \\\\\Rightarrow\rm Sum \: of\: numbers ={\boxed{\rm{658 }}}$

${\underline{\underline{\therefore{\text{Sum \: of \: 2 \: numbers = B)658 }}}}}$