Question

7 yr ago, the ages of A and B were in the ratio 4 : 5 and 7 yr hence, they will be in the ratio 5 : 6. The present age of A and B is
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Answer 1

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▪Given :-

• 7 years ago, the ages of A and B were in the ratio 4 : 5
• 7 years hence, they will be in the ratio 5 : 6.

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▪To Find :-

Present Ages of A and B.

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▪Solution :-

Let,

• Present Age of A be = x years
• Present Age of B be = y years

《 7 years Ago 》

• Age of A = (x -7) years

• Age of B = (y - 7) years

According to the Given Condition :

$\sf \dfrac{x - 7}{y - 7} = \dfrac{4}{5} \\ \\ \sf5(x - 7) = 4(y - 7) \\ \\ \sf 5x - 35 = 4y - 28 \\ \\ \large\bf 5x - 4y = 7 \: \: \: \:. \: . \: . \: \{i \}$

《 7 years Hence 》

• Age of A = (x + 7) years

• Age of B = (y + 7) years

According to the Given Condition :

$\sf \dfrac{x + 7}{y + 7} = \dfrac{5}{6} \\ \\ \sf6(x + 7) = 5(y + 7) \\ \\ \sf6x + 42 = 5y + 35 \\ \\ \large \bf6x - 5y = - 7 \: \: \: \:. \: . \:. \: \{ii \}$

Solving equations {i} and {ii}

We get,

$\Large\purple{ \underline {\boxed{{\bf x = 63 \: years} }}} \\ \\ \Large\purple{ \underline {\boxed{{\bf y = 77 \: years} }}}$

Hence,

• Present Age of A = 63 Years

• Present Age of B = 77 Years

$\Large \red{\mathfrak{  \text{W}hich \:   \: are  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswers.}}$

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Answer 2

Given :-

7 yr ago, the ages of A and B were in the ratio 4 : 5 and 7 yr hence, they will be in the ratio 5 : 6.

To Find :-

Present age of A and B

Solution :-

Let the age of A and B be 7 years ago be 4x and 5x

After 7 years their ages will be present age

Present age of A = 4x + 7

Present age of B = 5x + 7

After 7 year

Age of A = 4x + 7 + 7 = 4x + 14

Age of B = 5x + 7 + 7 = 5x + 14

Now

4x + 14/5x + 14 = 5/6

6(4x + 14) = 5(5x + 14)

24x + 84 = 25x + 70

24x - 25x = 70 - 84

-x = -14

x = 14

Present age of A = 4(14) + 7 = 56 + 7 = 63 years

Present age of B = 5(14) + 7 = 70 + 7 = 77 years