Question

4. Two numbers are in the ratio 7: 11. If 7 is added to each of the numbers, the ratio becomes 2: 3.
Find the numbers.
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Answer 1

Step-by-step explanation:

$\frak {Given} \begin{cases} &\sf{Two\ numbers\ are\ in\ the\ ratio\ of\ \bf 7\ :\ 11.} \\ &\sf{After\ number\ \bf 7\ \sf is\ added\ to\ each\ of\ the\ numbers\ the\ ratio\ becomes\ \bf 2\ :\ 3.} \end{cases}$

To find:- We have to find the numbers ?

☯️ The ratio is given as, 7 : 11. So, let the the first number be 7x and sacond number be 11x.

__________________

$\frak{\underline{\underline{\dag According\ to\ the\ question:-}}}$

$\sf : \implies {\bigg (\dfrac{7x\ +\ 7}{11x\ +\ 7}\ =\ \dfrac{2}{3} \bigg)} \\ \\ \\ \sf : \implies {\bigg (3(7x\ +\ 7)\ =\ 2(11x\ +\ 7) \bigg)} \\ \\ \\ \sf : \implies {21x\ +\ 21\ =\ 22x\ +\ 14} \\ \\ \\ \sf : \implies {22x\ -\ 21x\ =\ 21\ -\ 14} \\ \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf x\ =\ 7.}}}}\bigstar \\ \\ \\ \sf \therefore {\underline{The\ value\ of\ x\ is\ \bf 7.}}$

$\frak{\underline{\underline{\dag Now,\ finding\ the\ numbers:-}}}$

$\sf : \implies {First\ number\ =\ 7x\ =\ 7\ \times\ 7\ =\ \bf 49.}$

$\sf : \implies {Second\ number\ =\ 11x\ =\ 11\ \times\ 7\ =\ \bf 77.}$

Hence:-

$\sf \therefore {\underline{The\ required\ numbers\ are\ \bf 49\ \sf and\ \bf 77.}}$