The denominator of a fraction exceeds its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, we get \(\frac { 3 }{ 2 } \). Find the original fraction.

A number consists of two digits whose sum is 9. If 27 is subtracted from the original number, its digits are interchanged. Find the original number.

At present, Thenmozhi’s age is 5 years more than that of Murali’s age. Five years ago, the ratio of Thenmozhi’s age to Murali’s age was 3:2. Find their present ages.

A total of 90 currency notes, consisting only of Rs.5 and Rs.10 denominations, amount to Rs.500. Find the number of notes in each denomination.

The length of a rectangle is \(\frac { 1 }{ 3 } \) of its breadth. If its perimeter is 64m, then find the length and breadth of the rectangle.

The sum of three consecutive odd numbers is 75. Which is the largest among them?

One number is seven times another. If their difference is 18, find the numbers.

Find x and m: (i)\(\frac { 3x-2 }{ 4 } =\frac { (x-3) }{ 5 } =-1\) 
(ii) \(\frac { m+9 }{ 3m+15 } =\frac { 5 }{ 3 } \)

Find x: (i) – 3(4x + 9) = 21 (ii) 20 – 2 ( 5 – p) = 8 (iii) (7x – 5) – 4(2 + 5x) = 10(2 – x)

Find x and p: (i) \(\frac { 2x }{ 3 } \) - 4 = \(\frac { 10 }{ 3 } \) (ii) y+\(\frac { 1 }{ 6 } \) - 3y = \(\frac { 2 }{ 3 } \) (iii) \(\frac { 1 }{ 3 } -\frac { 1x }{ 3 } =\frac { 7x }{ 12 } +\frac { 5 }{ 4 } \)