Question

46. 10 year ago the ages of A and B were in the
ratio 13:17, respectively. 17 year from now the
respective ratioof their ages will be 10: 11. What
is the age of B at present?​

Answer 1

C) 27 yr

Description for Correct answer:

Let the ages of A and B 10 yr before were 13x yr and 17x yr, respectively.

Then, present age of A = 13x + 10 and present age of B = 17x + 10

According to the question,

13x+10+1717x+10+17=1011

13x+2717x+27=1011

Hence, present age of B = 17 x 1 + 10 = 27yr

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Answer 2

Answer:

Step-by-step explanation:

Given,

Ratio of ages of A and B , 10years ago = 13 : 17

Ratio of ages of A and B, after 17 years = 10 : 11

To Find:-

Present age of B.

Solution:-

Let,

the present age of :-

A be 'x'

B be 'y'

Given,

Ratio of ages of A and B , 10years ago = 13 : 17

Age of A ten years ago = x - 10

Age of B ten years ago = y - 10

$\implies \frac{x - 10}{y-10} = \frac{13}{17}$

let the constant be 'z'

x - 10 = 13z

x = 13x + 10

y - 10 = 17z

y = 17z + 10

Given,

Ratio of ages of A and B, after 17 years = 10 : 11

Age of A after 17 years = x + 17

Age of B after 17 years = y + 17

$\implies\frac{x + 17}{y+17} = \frac{10}{11}$

From above vlaues :-

$\implies \frac{13z + 10 + 17}{17z + 10 + 17} = \frac{10}{11}$

13z + 27/17z + 27 = 10/11

(13z + 27)11 = 10(17z + 27)

143z + 297 = 170z + 270

297 - 270 = 170z - 143z

27 = 27z

z = 27/27

z = 1

since,

Present age of B = y = 17z + 10

= 17(1) + 10

= 17 + 10

= 27

$\sf\therefore$ Present age of B = 27