Question
Nine years ago, the ratio of ages of Asha and Usha was
2:3, respectively. Seven years hence, the ratio of ages of Vimal and Usha will be 5:6, respectively. If Vimal is 4 years younger than Asha, find the age of Asha, 'a' years hence, where 'a' is the smallest two-digit even number.Solution
ATQ, Let the ages of Asha and Usha 9 years ago be 2x years and 3x years, respectively. Age of Vimal 9 years ago = 2x−4 years Age of Asha now = 2x+9 Age of Usha now = 3x+9 Seven years hence: Age of Asha = 2x+9+7=2x+16 Age of Usha = 3x+9+7=3x+16 Age of Vimal = 2x+16−4=2x+12 Given: (2x+12/3x+16) = (5/6) ​Solving the equation: 6×(2x+12)=5×(3x+16) 12x+72=15x+80 15x−12x=72−80 x=8 Since 10 is the smallest two-digit even number: Age of Asha, 10 years hence = 2x+9+10=2×8+9+10=35 years.
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