Question

the sum of one fifth of a number and one third of it next consecutive number is 3 what is the number​

Answer 1

ANSWER:-

Given:-

• The sum of one fifth of a number and one third of it next consecutive number is 3.

To Find:-

• The number.

So let the number be x. Therefore next consecutive number will be (x+1).

And one fifth of x = $\large\frac {x}{5}.$

Similarly one third of the next number = $\large\frac{x+1}{3}.$

So ATQ:-

$\tt\mapsto \frac{x}{5} + \frac{x + 1}{3} = 3. \\ \\ \tt\mapsto \frac{3(x) + 5(x + 1)}{(3)(5)} = 3. \\ \\ \tt(by \:taking \: lcm) \\ \\ \tt \mapsto \frac{3x + 5x + 5}{15} = 3. \\ \\ \tt\mapsto \frac{8x + 5}{15} = 3. \\ \\ \tt\mapsto8x + 5 = 3(15) \\ \\ \tt\mapsto8x + 5 = 45. \\ \\ \tt\mapsto8x = 45 - 5 .\\ \\ \tt\mapsto8x = 40. \\ \\ \tt\mapsto x = \frac{\cancel{40}}{\cancel8}. \\ \\ \tt\mapsto x = 5.$

$\therefore$ The number is x = 5.