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The sum of the present ages of Sarala and Kishore is 26 years. If 3 years ago, Kishore was 23тАЛ times as old as Sarala, then the present age of Sarala is:
10 years
9 years
12 years
11 years
11 years
Use the sum to express K in terms of S (K=26тИТS), substitute into the age difference equation, and solve for S. Since the ages are integers, options can also be tested: if S = 10, then K = 16. Three years ago: S-3=7, K-3=13 (Not 3/2). If S = 9, then K = 17. Three years ago: S-3=6, K-3=14 (Not 3/2). If S = 11, then K = 15. Three years ago: S-3=8, K-3=12. Here 12=23тАЛ├Ч8, which fits.
Sum of present ages of Sarala (S) and Kishore (K) is 26. Three years ago, Kishore's age was 3/2 times Sarala's age.
S+K=26, (KтИТ3)=23тАЛ(SтИТ3)
Use the sum to express K in terms of S (K=26тИТS), substitute into the age difference equation, and solve for S. Since the ages are integers, options can also be tested: if S = 10, then K = 16. Three years ago: S-3=7, K-3=13 (Not 3/2). If S = 9, then K = 17. Three years ago: S-3=6, K-3=14 (Not 3/2). If S = 11, then K = 15. Three years ago: S-3=8, K-3=12. Here 12=23тАЛ├Ч8, which fits.
Many students forget to subtract 3 from BOTH Sarala and Kishore when considering the condition '3 years ago'.
Define variables
Let the present age of Sarala be S and the present age of Kishore be K. From the problem, the sum is 26.
S+K=26тЯ╣K=26тИТS
Formulate the past age equation
Three years ago, their ages were (SтИТ3) and (KтИТ3). We are given that Kishore was 3/2 times as old as Sarala.
(KтИТ3)=23тАЛ(SтИТ3)
Substitute and solve for S
Substitute K=26тИТS into the second equation: (26тИТSтИТ3)=23тАЛ(SтИТ3). Simplify: 23тИТS=23тАЛ(SтИТ3). Multiply by 2: 46тИТ2S=3SтИТ9. Then 5S=55.
S=11
D is correct because solving the system of equations yields Sarala's present age as 11 years.
This type of age problem is fundamental to 'Linear Equations' and 'Ratio Analysis' in all competitive aptitude exams.
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