Question

The ratio of the ages of father and son at present is 6: 1. After 5 years the ratio will become 7:2. Find the present age of the son?
3 years
5 years
7 years
4 years

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Answer 1

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Let the present ages of father and his son be 6x years and x years respectively.

— After five years their ages;

Son's age = (x + 5) years

Father's age = (6x + 5) years

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$\large\underline\red{According \;to \;the \;given \;Question :}$

After five years, the ratio of their ages (father's age and son's age) will become 7: 2.

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Therefore,

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$:\implies\sf \bigg(\dfrac{6x + 5}{x + 5}\bigg) = \bigg(\dfrac{7}{2}\bigg)\\\\\\:\implies\sf 2(6x + 5) = 7(x + 5) \\\\\\:\implies\sf 12x + 10 = 7x + 35\\\\\\:\implies\sf 7x - 12x = 10 - 35\\\\\\:\implies\sf -5x = -25\\\\\\:\implies\sf x = \cancel\dfrac{-25}{-5}\\\\\\:\implies\underline{\boxed{\frak{\pink{x = 5}}}}\;\bigstar$

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Hence,

Present age of son = x = 5 years.

Present age of father = 6x = 6(5) = 30 years.

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$\therefore{\underline\red{\textsf{Hence, \; present\;age\;of\;son\; is\;\textbf{Option b) 5 years}.}}}$

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Answer 2

Answer:

The required present age of the son is (b) $5$ years

Step-by-step explanation:

Concept: Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio.

Given: The ratio of the ages of father and son at present is $6 : 1$

After $5$ years the ratio will become $7 : 2$

To find: The objective is to find out the present age of the son.

Solution:

Let the father and his son's current ages be $6x$ and $x$, respectively.

After five years their age:

Son's age$=(x+5)$ years

Father's age$=(6x+5)$ years

The ratio of their ages (the father's age to the son's age) will change to $7 : 2$ after five years.

$\frac{6x+5}{x+5} =\frac{7}{2}$

⇒$2(6x+5)=7(x+5)$

⇒$12x+10=7x+35$

⇒$-5x=-25$

⇒$x=5$

The Present age of the son's$=5$ years

The present age of the father $=(6$×$5)=30$ years

Therefore the required present age of the son is $5$ years.

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