Question

A's present age is to B's present age is 7:9. twelve years ago, their ages were in ratio 3:5 when would the ratio of their ages be 6:7​ by substitute method​

Answer 1

Solution :-

A's age - x ; B's age - y

Present age --

x/y = 7/9

x = 7y /9. (1)

Twelve years ago,

x-12 / y-12 = 3/5

5x - 60 = 3y - 36

by (1),

(7y/9)5 - 60 = 3y-36

35y /9 - 60 = 3y-36

(×9) 35y - 540 = 27y - 324

8y = 216

y = 27

x = 7y /9 (1)

= 7(27) / 9

= 7(3)

x = 21

A's age - 21 ; B's age - 27

when would the ratio of their ages be

6:7

Ratio of their ages be 6:7 when

x/y = 21×7/27×6

= 7×7 / 9×6

= 49 / 54

A's age is 49 ; B's age - 54

Answer 2

Answer:

In 15 years, the ratio of A and B's ages will be 6:7.

Step-by-step explanation:

A's present age to B's present age = 7 : 9

Ratio of their ages 12 years ago = 3 : 5

When would the ratio of their ages be 6 : 7

Let present ages of A and B be x and y respectively.

So, x : y = 7 : 9

$\sf{\longrightarrow} \: \dfrac{x}{y} = \dfrac{7}{9}$

$\sf{\longrightarrow} \:9x = 7y$

$\sf{\longrightarrow} \:x = \dfrac{7y}{9} \: - - - - (Eq.1)$

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Ages 12 years ago -

• A's age = (x - 12)
• B's age = (y - 12)

So, (x - 12) : (y - 12) = 3 : 5

$\sf{\longrightarrow} \: (x - 12) : (y - 12) = 3 : 5$

$\sf{\longrightarrow} \: \dfrac{ (x - 12)}{(y - 12) }= \dfrac{3}{5}$

$\sf{\longrightarrow} \:5(x - 12) = 3(y - 12)$

$\sf{\longrightarrow} \:5x - 60= 3y - 36$

$\sf{\longrightarrow} \:5x - 3y= - 36 + 60$

$\sf{\longrightarrow} \:5x - 3y = 24 \: - - - - (Eq.2)$

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Substitute Equation 1 in Equation 2,

$\sf{\longrightarrow} \:5\left( \dfrac{7y}{9}\right) - 3y = 24$

$\sf{\longrightarrow} \: \dfrac{35y}{9} - 3y = 24$

$\sf{\longrightarrow} \: \dfrac{35y - 27y}{9} = 24$

$\sf{\longrightarrow} \:8y = 24 \times 9$

$\sf{\longrightarrow} \:8y = 216$

$\sf{\longrightarrow} \:y = \dfrac{216}{8}$

$\sf{\longrightarrow} \:y = 27$

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Put the value of y in equation 1,

$\sf{\longrightarrow} \:x = \dfrac{7(27)}{9}$

$\sf{\longrightarrow} \:x = \dfrac{189}{9} = 21$

$\sf{\longrightarrow} \:x = 21$

Present ages of A and B is 21 and 27 years.

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Let after z years, ratio of A and B be 6 : 7.

$\sf{\longrightarrow} \: \dfrac{(21 + z)}{(27 + z)} = \dfrac{6}{7}$

$\sf{\longrightarrow} \:7(21 + z) = 6(27 + z)$

$\sf{\longrightarrow} \:147 + 7z = 162 + 6z$

$\sf{\longrightarrow} \:7z - 6z = 162 - 147$

$\sf{\longrightarrow} \:z = 15$

After 15 years, ages of A and B will be in ratio 6 : 7.

Therefore, In 15 years, the ratio of A and B's ages will be 6:7.