Age Difference Problem: Ayushi and Nidhi
Let Ayushi's present age be $A$ years and Nidhi's present age be $N$ years.
According to the problem statement:
- The difference between their present ages is 26 years. Since Ayushi is older, we have: $A - N = 26 \quad \tag{1}$
- Five years ago, their ages were $(A-5)$ and $(N-5)$ respectively. The sum of their ages five years ago was 30 years: $(A - 5) + (N - 5) = 30$ Simplifying this equation: $A + N - 10 = 30$ $A + N = 40 \quad \tag{2}$
Calculating Nidhi's Present Age
Now we have a system of two linear equations:
- $A - N = 26$
- $A + N = 40$
To find $N$, we can subtract Equation (1) from Equation (2):
$(A + N) - (A - N) = 40 - 26$ $A + N - A + N = 14$ $2N = 14$ $N = \frac{14}{2}$ $N = 7$Therefore, Nidhi's present age is 7 years.
To verify, we can find Ayushi's age using Equation (2): $A + 7 = 40 \implies A = 33$. The difference is $33 - 7 = 26$, and 5 years ago their ages were $33-5=28$ and $7-5=2$, summing to $28+2=30$. The conditions are met.
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