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

Two numbers are in the ratio of $3:5$. If $8$ is subtracted from each number, then the numbers are in the ratio of $1:3$. The second number is:

A sum of money is divided among A, B and C in such a way that the sum of the shares of A and B, B and C and C and A are, respectively, Rs. $12$, Rs. $14$ and Rs. $16$. What is B's share (in Rs.)?

The ratio of the number of boys and girls in a college consisting of $729$ students is $5:4$. How many girls should join the college so that the new ratio of the number of boys and girls is $1:1$?

If $a:b=7:6, b:c=5:4$ and $c:d=3:2$, then find $a:b:c:d$.

Gold is $19$ times as heavy as water and copper is $9$ times as heavy as water. In what ratio should gold and copper be mixed to form an alloy $14$ times as heavy as water?

Two tins A and B contain a mixture of wheat and rice. In A, the weight of wheat and rice is in the ratio of $2:3$ and in B the weight of wheat and rice is in the ratio of $3:7$. What quantity must be taken from the tins A and B to form a mixture containing $5$ kg of wheat and $11$ kg of rice?

About $729$ ml of a mixture contains milk and water in the ratio of $7:2$. How much water should be added to form a new mixture containing milk and water in the ratio of $7:3$?

About $6$ L of wine in a tank is replaced by $6$ L of water. Six litres of the mixture so formed is again replaced by $6$ L of water. If the ratio of wine to water in the tank at the end of the above replacements is $81:19$ then, what quantity of wine was there in the tank at the beginning of the operation? (There was no water in the tank at the beginning of the operation).