Question

the ratio of the ages of a and b four years ago was 4:5 eight years from now the ratio of the ages of a and b will be 11:13 what is the sum on their present ages​

Answer 1

⇝ Given :-

• The ratio of the ages of a and b four years ago was 4 : 5.

• Eight years from now the ratio of their ages will be 11 : 13.

⇝ To Find :-

• Sum of their Present Ages.

⇝ Solution :-

❒ Four Years Ago :

As The ratio of the ages of a and b four years ago was 4 : 5.

Therefore Let,

• Age of a = $\rm{4x}$ years

• Age of b = $\rm{5x}$ years

Therefore,

• Present Age of a = $\rm{(4x+4)}$ years

• Present Age of b = $\rm{(5x+4)}$ years

❒ Eight Years From Now :

• Age of a = $\rm{(4x+12)}$ years

• Age of b = $\rm{(5x+12)}$ years

⏩ According To Question :

$\large \red{ \rm \frac{4x+12}{5x+12 } = \frac{11}{13} }$

$:\longmapsto \rm 13(4x + 12) = 11(5x + 12)$

$:\longmapsto \rm 52x + 156 = 55x + 132$

$:\longmapsto \rm 55x - 52x = 156-132$

$:\longmapsto \rm 3x = 24$

$:\longmapsto \rm x = \cancel \frac{24}3$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 8} }}}$

Hence,

• Present Age of a = $\rm{(4x+4)}$ = 36 years

• Present Age of b = $\rm{(5x+4)}$ = 44 years

So,

Sum of Their Ages = 36 + 44

$\large\underline{\pink{\underline{\frak{\pmb{\text Sum \: of \: \text Their \: \text Ages = 80 \: \text years}}}}}$

Answer 2

Answer:

Question :-

• The ratio of ages of a and b four years ago was 4:5 .Eight years from now the ratio of ages of a and will be 11:13 . What is the sum on their present ages.

○Answer :-

• Answer will be The sum of their present ages is 80 years.

□Given :-

• The ratios of a and b four years ago was 4:5 .Eight years from now the ratio of ages of a and b will be 11:13 .

□To find :-

• The sum of their present ages.

□Solution :-

• In the question given that ,

♧《Four years ago》

• The ages becomes
• Age of a =4x=(4x+4)
• Age of B =5x=(5x+4)

♧《Eight years from now》

• The ages becomes,
• Age of a=(4x+4)=(4x+12)years.
• Age of B=(5x+4)=(5x+12) years.

• FROM THE QUESTION WE GET A EQUATION THAT IS ,

$\frac{4x + 12}{5x + 12} = \frac{11}{13}$

• $13(4x + 12) = 11(5x + 12)$

• $52x + 156 = 55x + 132$

• $55x - 52x = 156 - 132$

• $3x = 24$

• $x = \frac{24}{3}$

• $x = 8$

♧Therefore ,

• Present age of a=(4x+4)=(4(8)+4)=36 years.
• Present age of b =(5x+4)=(5 (4)+4)=44 years.

♧Hence,

• Sum of ages=36+44=80 years.

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♧Hope it helps u mate .

♧Thank you .