Question

the age of A and B are in the ratio 5:7.Four years from now the ratio of their age will be 3:4.Then the present age of B is​

Answer 1

Answer:

b's current age is 28 yrs

Step-by-step explanation:

for current yr

let common multiple be x

a = 5x, b = 7x

for after 4 yrs

let common multiple be y

a = 3y, b = 4y

therefore... 5x + 4 = 3y....(i) , 7x + 4 = 4y.....(ii)

subtracting equation i from ii we get

7x + 4. = 4y

- 5x. + 4. = 3y

(-) (-) (-)

ans: 2x. + 0. = y ......(iii)

substituting iii in i we get,

5x + 4 = 3(2x)

5x + 4 = 6x

4 = 6x - 5x

ans: x = 4.....iv

according to iv,

b's current age = 7x

= 7 * 4

= 28 yrs....ANSWER

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Answer 2

• Let present age of A be 5M

And

• Present age of B be 7M.

$\underline{Four \:years\: later..}$

• Age of A = 5M + 4

• Age of B = 7M + 4

And the $\underline{ratio \:of \:the \:ages\: of \:A \:and}$

$\underline{B\: is\: 3:4}$

A.T.Q.

$\Rightarrow \: \dfrac{5M\: + \: 4}{7M \: + \: 4} \: = \: \dfrac{3}{4}$

Cross-multiply them..

$\Rightarrow\:4(5M\:+\:4)\:=\:3(7M\:+\:4)$

$\Rightarrow\:20M\:+\:16\:=\:21M\:+\:12$

$\Rightarrow\:20M\:-\:21M\:=\:12\:-\:16$

$\Rightarrow\:-\:M\:=\:-\:4$

$\Rightarrow\:\boxed{M\:=\:4}$

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We have to find the present age of B.

So, from above calculations we get M = 4.

Now..

Present age of A = 5M

→ 5 × 4 = 20 years

Present age of B = 7M

→ 7 × 4 = 28 years.

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$\textbf{Present age of B is 28 years.}$

_________ [ ANSWER ]

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✡ $\textbf{Verification}$ :

From above calculations we get M = 4

Put value of M in this equation :

$\dfrac{5M\: + \: 4}{7M \: + \: 4} \: = \: \dfrac{3}{4}$

$\dfrac{5(4)\: + \: 4}{7(4) \: + \: 4} \: = \: \dfrac{3}{4}$

$\dfrac{20\: + \: 4}{28 \: + \: 4} \: = \: \dfrac{3}{4}$

$\dfrac{24}{32} \: = \: \dfrac{3}{4}$

$\dfrac{3}{4} \: = \: \dfrac{3}{4}$

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