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  • Question
  • The present ages of Vikas and Vishal are in the ratio 15:8. After ten years , their ages will be in the ratio 5:3. Find their present ages


  • Options
  • A. 60 years, 32 years
  • B. 32 years,60 years
  • C. 15 years,8 years
  • D. 8 years,15 years

  • Correct Answer
  • 60 years, 32 years 

    Explanation

    Method 1
    Let us assume the ratio factor is x.
    Therefor the present ages of Vikas and Vishal be 15x years and 8x years.
    After 10 years
    vikas's age = 15x + 10 and Vishal' age = 8x + 10
    According to question,
    (15x+10)/(8x+10) = 5/3
    ? 3(15x + 10) = 5(8x + 10)
    ? 45x + 30 = 40x + 50
    ? 5x =20
    ? x = 20/5
    ? x = 4
    Therefore Present age of Vikas = 15x = 15 x 4 = 60 years
    and Present age of Vishal = 8x = 8 x 4 = 32 years

    Method 2
    Let us assume the present age of Vikas = x years and Vishal's present year = y years
    According to question,
    Present age of Vikas/ Present age of Vishal = 15/8
    ? x/y = 15/8
    ? 8x = 15y
    ? 8x - 15y = 0
    ? x = 15y/8 .................................(1)
    After 10 years Vikash age = x + 10 and vishal age = y + 10
    Ratio of age after 10 years = 5/3
    (x + 10)/(y + 10) = 5/3
    ? 3(x + 10) = 5(y + 10)
    ? 3x + 30 = 5y + 50
    ? 3x - 5y = 50 - 30
    ? 3x - 5y = 20 ................................(2)
    Put the value of x from equation (1) in above equation (2).
    ? 45y/8 - 5y = 20
    ? 45y - 40y = 20 x 8
    ? 5y = 20 x 8
    ? y = 4 x 8 = 32
    Put the value of Y in equation (1)
    x = 15 x 32/8 = 15 x 4 = 60

    Therefore Present age of Vikas = x = 60 years
    and Present age of Vishal = y = 32 years


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    • Options
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