Embibe Experts Solutions for Exercise 1: Exercise 1

Three terms $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are said to be in proportion if _____.

If $(x:y)=2:1$, then$(x^2-y^2):(x^2+y^2)$ is _____.

Ram and Mohan are friends. Each has some money. If Ram gives $₹ 30$ to Mohan, then Mohan will have twice the money left with Ram. But if Mohan gives $₹ 10$ to Ram, then Ram will have thrice as much as is left with Mohan. How much money does each have$?$

Present age of John and Jack is in the ratio of $5:6$. if the John's age after two years and present age of Jack is in the ratio of $9:10$, then what is the sum of present ages of both John and Jack?

An express train travels $299 \mathrm{km}$, between two cities. During the first $111 \mathrm{km}$, of the trip, the train travelled through mountainous terrain. The train travelled $10 \mathrm{km}/\mathrm{h}$ , slower through mountainous terrain than through level terrain. If the total time to travel between two cities was $7 \mathrm{hour}$, what is the speed of the train on level terrain?

The speed of a train is $78 \mathrm{km}/\mathrm{h}$. It crosses a tunnel in $45 \sec$ and overtakes a person walking at a speed of $6 \mathrm{km}/\mathrm{h}$, in the same direction in $15 \sec$. The length of the tunnel is:

A train travel at a speed of $66 \mathrm{km}/\mathrm{h}$ and halt at five junctions for a certain time. It covers a distance of $1485 \mathrm{km}$ in one day. For how long does the train stop at each junction, if halts for the same period of time at all the junctions?

At his usual rowing rate, Ram can travel $12$ miles downstream in a certain river taking$6$ hour less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his $24$ mile round trip, the downstream $12$ miles would then take only one hour less than the upstream $12$ miles. What is the speed of the current in miles per hour?