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The ratio of the ages of Riya to Suman is 2:3. After 6 years from now, the ratio becomes 4:5. What is Riya's present age?
8 years
4 years
10 years
6 years
6 years
Observe the difference in ratios: (4тИТ2)=2 units and (5тИТ3)=2 units. Since both parts increased by 2 units corresponding to 6 years, 1 unit = 3 years. Riya's present age is 2├Ч3=6 years.
Initial age ratio of Riya to Suman is 2:3. After 6 years, the ratio becomes 4:5.
3x+62x+6тАЛ=54тАЛ
Observe the difference in ratios: (4тИТ2)=2 units and (5тИТ3)=2 units. Since both parts increased by 2 units corresponding to 6 years, 1 unit = 3 years. Riya's present age is 2├Ч3=6 years.
Students often make the mistake of adding 6 to the ratio components directly instead of adding it to the actual ages (2x and 3x).
Define ages in terms of x
Let the present ages of Riya and Suman be 2x and 3x respectively.
Riya=2x,Suman=3x
Set up the equation
After 6 years, the ages become (2x+6) and (3x+6), and their ratio is given as 4:5.
3x+62x+6тАЛ=54тАЛ
Solve for x
Cross-multiplying the equation gives 5(2x+6)=4(3x+6), which simplifies to 10x+30=12x+24.
2x=6тЯ╣x=3
Calculate Riya's age
Substitute x=3 back into the initial expression for Riya's age, which is 2x.
RiyaтАЩs┬аAge=2├Ч3=6
D is correct because solving the ratio equation 3x+62x+6тАЛ=54тАЛ yields x=3, making Riya's present age 2(3)=6 years.
This unit-difference method is highly effective for Partnership and Mixture problems where quantities change by a fixed amount over time.
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