Question

if the same number be added to the number 5,11,15 and 31.The resulting number are in proportion. find the number.
​

Answer 1

Step-by-step explanation:

Answer

AnswerLet The number be x

AnswerLet The number be x11+x

AnswerLet The number be x11+x5+x

AnswerLet The number be x11+x5+x

AnswerLet The number be x11+x5+x =

AnswerLet The number be x11+x5+x = 31+x

AnswerLet The number be x11+x5+x = 31+x15+x

AnswerLet The number be x11+x5+x = 31+x15+x

AnswerLet The number be x11+x5+x = 31+x15+x

AnswerLet The number be x11+x5+x = 31+x15+x ⇒155+x

AnswerLet The number be x11+x5+x = 31+x15+x ⇒155+x 2

AnswerLet The number be x11+x5+x = 31+x15+x ⇒155+x 2 +36x=165+x

AnswerLet The number be x11+x5+x = 31+x15+x ⇒155+x 2 +36x=165+x 2

AnswerLet The number be x11+x5+x = 31+x15+x ⇒155+x 2 +36x=165+x 2 +26x

AnswerLet The number be x11+x5+x = 31+x15+x ⇒155+x 2 +36x=165+x 2 +26x10x=10

AnswerLet The number be x11+x5+x = 31+x15+x ⇒155+x 2 +36x=165+x 2 +26x10x=10x=1

AnswerLet The number be x11+x5+x = 31+x15+x ⇒155+x 2 +36x=165+x 2 +26x10x=10x=1∴ Numbers are 5+1=6, 11+1=12

AnswerLet The number be x11+x5+x = 31+x15+x ⇒155+x 2 +36x=165+x 2 +26x10x=10x=1∴ Numbers are 5+1=6, 11+1=12 15+1=16, 31+1=32.

PLEASE MARK ME AS BRAINLIST

Answer 2

Your Question :

If the same number be added to the numbers 5,11,15 and 31 then the resultant numbers are in proportion. Find the number.

Stepwise Solution :

Let the number be x.

Then, 5 + x, 11 + x, 15 + x and 31 + x are in proportion. That is,

$\sf{{⟹ \: \frac{5 + x}{11 + x} = \frac{15 + x}{31 + x} \: }{ \: }}$

$\sf{{ ⟹\:(5 + x)(31 + x) = (11 + x)(15 + x) }{ \: }}$

$\sf{{⟹ \: 115 + 36x + {x}^{2} = 165 + 26x + {x}^{2} }{ \: }}$

$\sf{{⟹ \: 36x - 26x = 165 - 155 }{ \: }}$

$\sf{{⟹ \: 10x = 10 }{ \: }}$

$\sf{{ ⟹\: x = \frac{10}{10} = 1 }{ \: }}$

Final Answer :

∴ The required number is 1.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬