Embibe Experts Solutions for Chapter: Ratio and Proportion, Exercise 1: Exercise 1

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

If $(a+b) : \sqrt{ab}=4 : 1$, where $a > b > 0$, then find the ratio $a : b$.

A sum of money $₹730$ were divided among $A, B, C$ in such a way that if $A$ gets $₹3$, then $B$ gets $₹4$ and if $B$ gets $₹3.50$ then $C$ gets $₹3$. The share of $B$ exceeds that of $C$ by what amount?

A man gave $50\%$ of his savings of $₹84100$ to his wife and divided the remaining sum among his two sons $A$ and $B$ of $15 \mathrm{years}$ and $13 \mathrm{years}$ of age respectively. He divided it in such a way that each of his sons when they attain the age of $20 \mathrm{years}$, would receive the same amount at $5\%$ compound interest per annum. Find the share of $B$.

If $2A=3 B=4C$, then find $A : B : C$.

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?

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?