Question

if the denominator of a fraction is in reased by 4 then the fraction becomes 5/8.if the numerator is 11 less than the denominator find the numerator​

Answer 1

let the denominated be X

then numerator will be x-11

according to the ques

(x-11)/X+4=5/8

5x+20=8x-88

3x=108

X=36

Answer 2

GIVEN :-

• Numerator of a fraction is 11 less than the denominator and if the denominator is increased by 4 then fraction becomes 5/8

TO FIND :-

• The numerator of the fraction

SOLUTION :-

Let ,

• 'x' be the denominator of the fraction
• Then numerator becomes ' x - 11 '

Denominator when increased by 4 becomes ' x + 4 '

According to the question ,

$\large \sf \dfrac{x - 11}{x + 4} = \dfrac{5}{8} \\ \\ \implies \sf \: 5(x + 4) = 8(x - 11) \\ \\ \implies \sf \: 8x - 88= 5x + 20 \\ \\ \implies \sf \: 8x - 5x = 88 + 20 \\ \\ \implies \sf \: 3x = 108 \\ \\ \implies \sf \: x = \frac{ 108}{3} \\ \\ \implies {\underline {\boxed {\blue{\sf{x = 36 }}}}}$

Then ,

$\sf \: denominator \:of \: the \: fraction = x = 36 \\ \\ \sf \: numerator \: of \: the \: fraction = x - 11 = 36 - 11 = 25 \\ \\ \implies \sf \: fraction = \frac{numerator}{denomintor} \\ \\ \implies {\underline {\boxed {\blue {\sf{fraction = \frac{25}{36} }}}}}$

∴ The numerator of the fraction = 25

VERIFICATION :-

If the given fraction was 25/36 then ,

• numerator = 25
• denominator = 36

(1) First condition ,

Numerator should be 11 less than the denominator

36-11 = 25 ✓

(2) Denominator when increased by 4 = 40

Then fraction = 25/40 = 5/8 ✓

Since all conditions are true

∴ The fraction is 25/36

and Numerator is 25

$\huge{\underline {\boxed {\green {\rm{HENCE\:VERIFIED}}}}}$