Math, asked by 271333so, 10 months ago

five year's ago, A's age was 5 years less than twice B's age. three years from now,one third of B's age will be 12 years less than A's age find their present ages

Answers

Answered by MяƖиνιѕιвʟє
124

\bf{\red{\underline{\bf{Given}}}}

  • Five year's ago, A's age was 5 years less than twice B's age. three years from now,one third of B's age will be 12 years less than A's age.

\bf{\red{\underline{\bf{ToFind}}}}

Present ages of :-

  • A and B

\bf{\red{\underline{\bf{Solution}}}}

Let present age of A be x years and B be y years

then,

According to 1st condition :-

5 - years ago,

  • A's age = (x - 5) years
  • B's age = ( y - 5) years

A's age = 2(B's age) - 5

(x - 5) = 2 (y - 5) - 5

x - 5 = 2y - 10 - 5

x - 5 = 2y - 15

x = 2y - 15 + 5

x = 2y - 10. --(1)

\rule{200}2

According to 2nd condition :-

3 - years later,

  • A's age = (x + 3) years
  • B's age = (y + 3) years

1/3 ( B's age) = (A's age) - 12

1/3 × (y + 3) = (x + 3) - 12

(y + 3)/3 = x - 9

y + 3 = 3(x - 9)

y + 3 = 3x - 27

y = 3x - 27 - 3

y = 3x - 30. --(2)

\rule{200}2

Put value of (1) in (2) , we get ,

y = 3x - 30

y = 3(2y - 10) - 30

y = 6y - 30 - 30

6y - y = 60

5y = 60

y = 60/5

y = 12

Put y = 12 in (1) , we get,

x = 2y - 10

x = 2×12 - 10

x = 24 - 10

x = 14

Hence,

  • A's age = x = 14 years
  • B's age = y = 12 years

\rule{200}3

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