Question

10 years ago the age of A and B were in the ratio 13 ratio 17 respect 17 years from now the respective ratio is of the age will be 10 ratio 11 what is the age of be at present​

Answer 1

AnswEr:-

Present age of B = 27 years.

$\rule{200}{1}$

Let present age of A & B be m & n years respectively.

• 10 years ago,present age of A & B = 13 : 17

⇒ (m - 10) : (n - 10) = 13 : 17

⇒ (m - 10)/(n - 10) = 13/17

⇒ 13(n - 10) = 17(m - 10)

⇒ 13n - 130 = 17m - 170

⇒ 17m - 170 = 13n - 130

⇒ 17m - 13n = -130 + 170

⇒ 17m - 13n = 40 -(Eq.1)

• 17 years from now,age of A & B = 10 : 11

⇒ (m + 17) : (n + 17) = 10 : 11

⇒ (m + 17)/(n + 17) = 10/11

⇒ 11(m + 17) = 10(n + 17)

⇒ 11m + 187 = 10n + 170

⇒ 11m - 10n = 170 - 187

⇒ 11m - 10n = -17 -(Eq.2)

By multiplying (Eq.1) by 10 & (Eq.2) by 13 we get:-

⇒ 170m - 130n = 400 ---(Eq.1)

⇒ 143m - 130n = -221 ----(Eq.2)

Now substracting (Eq.2) from (Eq.1) :-

⇒ 170m - 130n - 143m + 130n = 400 + 221

⇒ 27m = 621

⇒ m = 621/27

⇒ m = 23 years.

Now putting this value in (Eq.2):-

⇒ 11(23) - 10n = -17

⇒ 253 - 10n = -17

⇒ -10n = -17 - 253

⇒ -10n = -270

⇒ n = - 270/- 10

⇒ n = 27 years.

∴ Present age of B = 27 years.

Answer 2

Answer:

Present age of B is 27.

Step-by-step explanation:

As per the question,

Let 10 years ago age of A = 13x

and 10 years age of B = 17x

Hence present age of A will be = 13x + 10

subsequently B will be = 17x + 10

same way after 17 years from now age of A will be = 13x + 27

and age of B will be = 17x + 27

Ratio of age of A & B after 17 years is 10:11

Hence, 13x+27 / 17x+27 = 10 / 11

=> 143x+297 = 170x+270

=> 27x = 27

=> x = 27

So, Present age of B = 17x + 10 = 27

Hope this will clear your doubt :)