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

2 thoughts on “46. 10 year ago the ages of A and B were in the<br />ratio 13:17, respectively. 17 year from now the<br />respective ratioof their”

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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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

   [tex]\implies \frac{x – 10}{y-10} = \frac{13}{17}[/tex]

   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

   [tex]\implies\frac{x + 17}{y+17} = \frac{10}{11}[/tex]

   From above vlaues :-

   [tex]\implies \frac{13z + 10 + 17}{17z + 10 + 17} = \frac{10}{11}[/tex]

   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

   [tex]\sf\therefore[/tex] Present age of B = 27

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