Embibe Experts Solutions for Chapter: Time and Work, Exercise 1: IOQM - PRMO and RMO 2019 (25-08-2019)

Two people $A$ and $B$ start from the same place at the same time to travel around a circular track of length $100$ metre in opposite directions. First $B$ goes more slowly than $A$ until they meet, then by doubling his rate he next meets $A$ at the starting point. Let $d$ metre be the distance travelled by $B$ before he met $A$ for the first time after leaving the starting point. Find the Integer closest to $d$.

On a clock, there are two instants between $12$ noon and $1$ PM, when the hour hand and the minute hand are at right angles. The difference in minutes between these two instants is written as $a+\frac{b}{c},$ where $a, b \text{and} c$ are positive integers, with $b<c$ and $\frac{L}{c}$ in the reduced form. What is the value of $a+b+c?$

One day I went for a walk in the morning at $x$ minutes past $5\text{'}O$ clock, where $x$ is a two-digit number. When I returned, it was $y$ minutes past $6\text{'}O$ clock, and I noticed that $\left(\mathrm{i}\right)$ I walked exactly for $x$ minutes and $\left(\mathrm{ii}\right)$ $y$ was a $2$-digit number obtained by reversing the digits of $x$. How many minutes did I walk?