Three-fourths of one-fifth of a number is $60$. The number is:

If the digit in the unit's place of a two-digit number is halved and the digit in the ten's place is doubled,the number thus obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true?

$\frac{3}{5}$ th of $24 \%$ of $500 - 32 = ?$

The difference between one-fourth of a number and one-seventh of the same number is $24$. What is the number?

$A$ fraction becomes $4$ when $1$ is added to both the numerator and denominator; and it becomes $7$ when $1$ is subtracted from both the numerator and denominator. The numerator of the given fraction is

$\frac{1}{4}$ of a number subtracted from $\frac{1}{3}$ of the same number gives $12$. The number is: