Cengage Experts Team (CET) Solutions for Exercise 1: Practice Exercise

One test-tube contains some acid and another test tube contains an equal quantity of water. To prepare a solution, $20$ ml of acid is poured into the second test tube from the first test tube. Then, two-third of the solution so-formed was poured from the second test tube into the first. If the solution in the first test tube is $4$ times that in the second, then what quantity of water was taken initially in the first test tube?

There are two examination rooms A and B. If $10$ students are shifted from A to B, then the number of students in each room is the same. If $20$ candidates are shifted from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

$N$ number of persons contributed equally to raise $₹3$ lakhs. Had each person contributed $₹500$ extra, the total contribution would have been $₹5.5$ lakhs. How many persons contributed the money?

Eight persons equally share the cost of renting a car. If one person withdraws from the agreement and the others agree to share the entire cost of renting the car equally, then the share of each of the remaining persons increases by what part of his or her original share:

In a classroom, if $6$students sit on every bench, then $1$ more bench is required to accommodate all the students. However, if $7$ students sit on every bench, then there is space for$5$ more students. What is the number of students in the class?

In a certain shop $6$ oranges cost as much as the cost of $5$ apples, $5$ apples cost as much as the cost of $3$mangoes and $3$mangoes cost as much as the cost of$6$bananas. If $3$bananas cost $\mathrm{Rs}.4.80$, the price of an orange is:

It costs Rs.$x$ per shirt to stitch the first thousand shirts and Rs.$y$ to stitch each subsequent shirt. If $z$ is greater than $1,000$, how much will it cost to stitch $z$number of shirts?

The taxi charges for a journey comprises a fixed charge and a variable charge which is according to the distance covered. For a journey of $15$ km, the charges paid are Rs.$125$ and for a journey of $25$ km, the charges paid are Rs.$175.$ What are the taxi charges for a journey of $30$km?