Question

22. If the numerator and the denominator of a fraction
are each increased by 4, the fraction becomes 2
and when numerator and denominator of the same
fraction are each decreased by 6, the fraction
becomes 12. The sum of the numerator and the
denominator is
(1) 11 (2) -11
(3) 25 (4) -25​

Answer 1

Answer:

step by step explanation pls mark me as the brainleist

Answer 2

${\large{\underline{\pmb{\frak{Given...}}}}}$

✰ the numerator and the denominator of a fraction  are each increased by 4, the fraction becomes 2

✰ And when numerator and denominator of the same  fraction are each decreased by 6, the fraction  becomes 12

${\large{\underline{\pmb{\frak{To \; Find...}}}}}$

✰ The sum of the numerator and the  denominator of the fraction

${\large{\underline{\pmb{\frak{Let's \; Understand \; the \; concept...}}}}}$

☀️ Concept : As we have given two statements related to thee fraction which are that ,

⠀⠀⠀⠀⠀⠀⠀⠀⋆  If the numerator and the denominator of a fraction are each increased by 4, the fraction becomes 2

⠀⠀⠀⠀⠀⠀⠀⠀⋆ And when numerator and denominator of the same  fraction are each decreased by 6, the fraction  becomes 12

❍ Now let's frame equations according to the statement assigning suitable variables to the numerator and the denominator as they are undefined and then use substitution  method to solve them.

                           

${\large{\underline{\pmb{\sf{RequirEd \; Solution...}}}}}$

✰ The sum of the numerator and the denominator of thee fraction is 25

${\large{\underline{\pmb{\frak{Full \; solution...}}}}}$

★ Now let us assume that,

⠀⠀⠀⠀⠀⠀» Numerator of the fraction is x

⠀⠀⠀⠀⠀⠀» Denominator of the fraction is y

~ Framing an equation according to the first statement,

$\longrightarrow \tt \dfrac{x+4}{y+4} = \dfrac{2}{1}$

→ Now let's cross multiply the fractions and frame an equation,

$\longrightarrow \tt 1( x + 4 ) = 2( y + 4 )$

$\longrightarrow \tt x - 2y = 4 ---( 1)$

~ Framing an equation according to the second statement,

$\longrightarrow \tt \dfrac{x-6}{y-6} = \dfrac{12}{1}$

→ Now let's cross multiply the fractions and frame an equation,

$\longrightarrow \tt x - 6 = 12y - 72$

$\longrightarrow \tt x - 12y = -72 + 6$

$\longrightarrow \tt x - 12y = -66 ---(2)$

~ From equation one let's find out the value of x in terms of the variable y

$\longrightarrow \tt x - 2y = 4$

$\longrightarrow \tt x = 2y + 4$

~ Now let's substitute the value of x in equation 2 and find the value of y

$\longrightarrow \tt x - 12 y = -66$

$\longrightarrow \tt 2y + 4 - 12y = - 66$

$\longrightarrow \tt - 10 y - 4 = - 66$

$\longrightarrow \tt - 10 y = -66 - 4$

$\longrightarrow \tt - 10 y = - 70$

$\longrightarrow \tt y = \dfrac{-70}{-10}$

$\longrightarrow \tt y = 7$

• Henceforth the denominator of the fraction is 7

~ Now let's substitute the value of y in equation 1 and find the value of x

$\longrightarrow \tt x - 2y = 4$

$\longrightarrow \tt x - 2(7) = 4$

$\longrightarrow \tt x - 14 = 4$

$\longrightarrow \tt x = 4 + 14$

$\longrightarrow \tt x = 18$

• Henceforth the numerator of the fraction is 18

~ Now let's find the sum of the numerator and the denominator

→ 7 + 18

→ 25

• Henceforth the sum of the numerator and the denominator is 25