Question

Three years ago, the ratio of ages of A and B was 7:1. After three years from noww, the ratio of their ages will be 4:1. What is the difference between their ages (in years) after seven years from now?​

Answer 1

Answer:

difference = 7 years

Step-by-step explanation:

Please refer to the image

Answer 2

▪ Given :- 

☆》Three years ago, the ratio of ages of A and B was 7:1.

☆》After three years from now, the ratio of their ages will be 4:1.

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▪To Calculate :-

The difference between their ages after seven years from now

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▪ Solution :-

Let ,

Present age of A be = x years

And ,

Present age of B be = y years

《 3 years ago 》

Age of A = (x - 3) years

And ,

Age of B = (y - 3) years

According to the Given Condition :

$\dfrac{x - 3}{y - 3} = \dfrac{7}{1} \\ \\ x - 3 = 7(y - 3) \\ \\ x - 3 = 7y - 21 \\ \\ \large \bf x - 7y = - 18 \: \: \: \: .\: . \: . \: \{i \}$

《 3 years from now 》

Age of A = (x + 3) years

And ,

Age of B = (y + 3) years

According to the Given Condition :

$\dfrac{x + 3}{y + 3} = \dfrac{4}{1} \\ \\ x + 3 = 4(y + 3) \\ \\ x + 3 = 4y + 12 \\ \\ \large \bf x - 4y = 9 \: \: \: \:. \: .\: .\: \{ii \}$

Subtracting {i} from {ii} We Get ,

$3y = 27 \\ \\ \large \purple{ \implies  \underline {\boxed{{\bf y = 9 \: years} }}}$

Putting Value of y in {i}

$x - 4 \times 9 = 9 \\ \\ \purple{ \implies  \underline {\boxed{{\bf x = 45\: years} }}}$

《 7 years from now 》

$\bf Age \: of \: A = (x + 7) years \\ \\ \bf = 52 \: years \\ \\ \bf And , \\ \\ \bf Age \: of \: B = (y + 7) years \\ \\ \bf = 16 \: years$

$\huge \mathcal{So,}$

Difference between their ages

= 52 - 16

= 36 years

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

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