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:

1. $A - N = 26$
2. $A + N = 40$

To find $N$, we can subtract Equation (1) from Equation (2):

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.