PUNE MCA Exam 2015 Question Paper with answers for online practice

Concept:Set up equations for ages and digit reversal, then solve for integer ages.Explanation:Let $N$, $G$, $E$ be ages of Newton, Galileo, Einstein.Given: $N = 10G$ and $N$ is the reverse of $E$.Also $|E - N| = 2G$.Substitute $G = N/10$ into the difference: $|E - N| = N/5$.So $E = N \pm N/5 = \frac{6}{5}N$ or $\frac{4}{5}N$.Thus $N$ must be a multiple of $5$. Also $N = 10G$ is multiple of $10$, so $N$ is multiple of $10$.Let $N = 10k$, then $E = 12k$ or $8k$.Since $N$ is the reverse of $E$, we need $E$ to have digits that reversed give $N$.Check small multiples: For $k=1$ to $9$, $N=10,20,...,90$ and $E$ (if $12k$) gives $12,24,...,108$. The reverse of $N$ (e.g., $10$ reversed is $01=1$) does not equal $E$.For $k\geq10$, $N$ has more digits, but the reversed $N$ always has fewer digits because $N$ ends with $0$. This never matches $E$.No integer solution exists for any age satisfying all conditions.Answer:No valid age of Einstein among given ranges.