Embibe Experts Solutions for Chapter: Algebra, Exercise 5: EXERCISE - 1.5

Each valve $A, B$, and $C$, when open, releases water into a tank as it own constant rate. With all three valves open, the tank fills in $1$ hour, with only valves $A$ and $C$ open it takes $1.5$ hour, and with only valves $B$ and $C$ open it takes $2$ hours. The number of minutes required with only valves $A$ and $B$ open is

Mohit has a collection of $23$ coins, consisting of $5$-paise coins, $10$-paise coins, and $25$-paise coins. He has $3$ more $10$-paise coins than $5$-paise coins, and the total value of his collection is $320$ paise. How many more $25$-paise coins does Mohit have than $5$-paise coins?

Sameer drive $96 \mathrm{km}$ in $90 \mathrm{mins}$. His average speed during the first $30 \mathrm{mins}$ was $60 \mathrm{kph}$ (kilo meter per hour), and his average speed during the second $30 \mathrm{mins}$ was $65 \mathrm{kph}$. What was his average speed, in $\mathrm{kph}$, during the last $30 \mathrm{mins}$?

Every week Ramesh pays for a movie ticket and a soda out of his allowance. Last week, Ramesh's allowance was $A$ Rupees. The cost of his movie ticket was $20\%$ of the difference between $A$ and the cost of his soda, while the cost of his soda was $5\%$ of the difference between $A$ and the cost of his movie ticket. To the nearest whole percent, what fraction of $A$ did Ramesh pay for his movie ticket and soda?

Consider the set of all fractions $\frac{x}{y}$, where $x$ and $y$ are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by $1$, the value of the fraction is increased by $10\%$?

Suppose that $4$ cows give $10$ gallons of milk in $2$ days. At this rate, how many gallons of milk will $5$ cows give in $4$ days?

Hari drives from his home to the airport to catch a flight. He drives $35 \mathrm{km}$ in the first hour, but realizes that he will be $1$ hour late if he continues at this speed. He increases his speed by $15 \mathrm{km}$ per hour for the rest of the way to the airport and arrives $30$ minutes early. If the distance between the airport and his home is $P \mathrm{km}$. Find $\frac{P}{7}$.

Divya drove her new car on a trip for a whole number of hours, averaging $55 \mathrm{km}$ per hour. At the beginning of the trip, $abc \mathrm{km}$ were displayed on the odometer, where $a b c$ is a $3$-digit number with $a\ge 1$ and $a+b+c\le 7$. At the end of the trip, where the odometer showed $cba$ $\mathrm{km}$. What is $a^2+b^2+c^2$?