Multiple choice

Virat and Rohit are brothers. Four years ago, the ratio of the ages of Virat and Rohit was 10 : 18. Eight years hence, the ratio will be 2 : 3, respectively. Find the present age of Rohit.

  1. 50 years

  2. 36 years

  3. 40 years

  4. 20 years

  5. 25 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ages 4 years ago be 10x and 18x. Present ages: 10x+4, 18x+4. (10x+4+8)/(18x+4+8) = 2/3. (10x+12)/(18x+12) = 2/3. 30x+36 = 36x+24. 6x = 12, x = 2. Rohit's present age = 18(2)+4 = 40.

AI explanation

Let the present ages of Virat and Rohit be V and R. Four years ago, the ratio of their ages was 10 to 18, meaning (V minus 4) divided by (R minus 4) equals 10 divided by 18, which simplifies to the equation 18V minus 10R equals 32. Eight years hence, the ratio will be 2 to 3, meaning (V + 8) divided by (R + 8) equals 2 divided by 3, which simplifies to the equation 3V minus 2R equals negative 8. Solving these two linear equations simultaneously yields R equal to 40, making Rohit's present age 40 years.

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