Question

The ratio of the age of goat and sheep at present is 7:17. If after 20 years the ratio will become 9:19 then what is the present age of the goat? 4/30 questions attempted​

Answer 1

Answer:

Let the present age of goat be 7x

Sheep be 17x

According to question:-

$\frac{7x + 20}{17x + 20} = \frac{9}{19}$

$= 19(7x + 20) = 9(17x + 20)$

=133x+380=153x+180

=380-180=153x-133x

200=20x

$x = \frac{200}{20}$

x=10

Present age of goat=7x

=7(10)years

=70 years

Present age of sheep= 17x

Present age of sheep= 17x=17(10) years

) years=170 years

Answer 2

Given,

The present ratio of the age of goat and sheep$\[ = 7:17\]$

After twenty years, the ratio of the age of goat and sheep$\[ = 9:19\]$

Solution,

Assume that the age of goat is $\[7x\]$ and sheep is $\[17x.\]$

Consider the second condition,

$\[\begin{array}{l} \Rightarrow \frac{{7x + 20}}{{17x + 20}} = \frac{9}{{19}}\\ \Rightarrow 133x + 380 = 153x + 180\\ \Rightarrow 153x - 133x = 380 - 180\end{array}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow 20x = 200\\ \Rightarrow x = \frac{{200}}{{20}}\\ \Rightarrow x = 10\end{array}\]$

Therefore, the present age of the goat is

$\[\begin{array}{l} = 10 \times 7\\ = 70\end{array}\]$

Hence, the present age of the goat is $\[70{\rm{years}}{\rm{.}}\]$