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The present Age of Rohit and Mayank are in the Ratio 11:8.8 years later the sum of their ages will be 54 years. what are their present ages ?
Let, Rohit's present age = 11 x
Mayank's present age = 8x
8 years later,
Rohit's age = 11x + 8
Mayank's age = 8x + 8
11x + 8 + 8x +8 = 54
19x + 16 = 54
19x = 38
x = 2
Rohit's age = 11 × 2 = 22 years
Mayank's age = 8 × 2 = 16 years
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A father's age is 3 times the sum of ages of his two sons. 5 years later he will be twice the sum of ages of his two sons. Find the present age of the father.
let the age of two sons = x
According to the question
Father's age = 3 × x
After 5 years,
two son = x + 5
father's age = 3x +5
According to the question
Age of father = 3 × 5
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Answer:
\large{{ \bold{ \underline{Question.1 \: \: }}}}
Question.1
The present Age of Rohit and Mayank are in the Ratio 11:8.8 years later the sum of their ages will be 54 years. what are their present ages ?
\large{ \bold{ \underline{Given: - }}}
Given:−
Ratio ages of Rohit nad Mayank 11:8
\large{ \bold{ \underline{To \: Find : - }}}
ToFind:−
Their present ages .
\large{ \bold { \underline{Solution : - }}}
Solution:−
: \implies:⟹ Let, Rohit's present age = 11 x
: \implies:⟹ Mayank's present age = 8x
8 years later,
: \implies:⟹ Rohit's age = 11x + 8
: \implies:⟹ Mayank's age = 8x + 8
\therefore∴ 11x + 8 + 8x +8 = 54
: \implies:⟹ 19x + 16 = 54
: \implies:⟹ 19x = 38
: \implies:⟹ x = 2
\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large\bold{ \blue{ :\implies}}:⟹ Rohit's age = 11 × 2 = 22 years
\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large{ \bold{ \blue{ :\implies}}}:⟹ Mayank's age = 8 × 2 = 16 years
\: \: \: \: \: \: \large{ \boxed{ \mathfrak{ \red{Answer :- \ present \: ages \: are \: 22 \: and \: 16 years.}}}}
Answer:− presentagesare22and16years.
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\large \bold{ \color{black}{ \underline{Question.2 \: \: }}}
Question.2
A father's age is 3 times the sum of ages of his two sons. 5 years later he will be twice the sum of ages of his two sons. Find the present age of the father.
\large{ \bold{ \underline{ \color{black}{Given : - }}}}
Given:−
Relation of ages between son and father.
\large{ \bold{ \underline{ \color{black}{To \: Find : - }}}}
ToFind:−
Present age of father
\large{ \bold{ \underline{ \color{black}{Solution : - }}}}
Solution:−
\: \: \: \: \: \: : \implies:⟹ let the age of two sons = x
According to the question
\: \: \: \: \: \: : \implies:⟹ Father's age = 3 × x
After 5 years,
\: \: \: \: \: \: : \implies:⟹ two son = x + 5
\: \: \: \: \: \: : \implies:⟹ father's age = 3x +5
According to the question
\begin{gathered} \: \: \: \: \: \: \: \: \: \: : \implies \sf(3x + 5) = (x + 5) \times 2 \\ \\ \: \: \: \: \: \: \: \: \: : \implies \sf3x + 5 = 2x + 10 \\ \\ \: \: \: \: \: \: : \implies \sf \: x \: = 5\end{gathered}
:⟹(3x+5)=(x+5)×2
:⟹3x+5=2x+10
:⟹x=5
Age of father = 3 × 5
\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sf \: 15 \: years=15years
\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large{ \boxed{ \mathfrak{ \pink{Hence, \: the \: age \: of \: father \: is \: 15 \: years.}}}}
Hence,theageoffatheris15years.
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