T. S. Jain Solutions for Exercise 1: Exercise

Two numbers are such that the sum of twice the first number and thrice the second number is $36$ and the sum of thrice the first number and twice the second number is $39$. Which is the smaller number?

The sum of the digits of a two-digit number is $12$. If the new number formed by reversing the digit is greater than the original number by $54$ then what will be the original number?

If the fractions $\frac{2}{5}, \frac{3}{8}, \frac{4}{9}, \frac{5}{13}$ and $\frac{6}{11}$ are arranged in ascending order of their values, which one will be the fourth?

The sum of the square of the first number and the cube of the second number is $568$ together. Also square of the second number is $15$ less than the square of $8$. What is the value of three-fifth of the first number? (assuming both the numbers are positive)

One-fifth of a number is $81$. What will $68\%$ of that number be?

By how much is $\frac{5}{12}$th of $516$ lesser than $\frac{4}{9}$th of $495$?

The number obtained by interchanging the digits of a two-digit number is less than the original number by $63$. If the sum of the digits of the number is $11$, what is the original number?

If the numerator of a fraction is increased by $200\%$ and the denominator is increased by $300\%$, the resultant fraction is $\frac{15}{26}$. What was the original fraction?