Question

one-third of the length of a pole is underground, one-fifth is in water and the remaning 7m is above water. How long is the pole?

Answer 1

Let the total length of the pole is x m ,




According to the question ,



Length of pole under the ground = 1 / 3 of x m

$= \frac{1}{3} \times x \: \: m = \frac{x}{3} \: \: m$



Length of pole which is in water = 1 / 5 of x

$= \frac{1}{5} \times x \: \: \: m= \frac{x}{5} \: \: \: m$



Remaining length or length of pole above the water = 7 m






Total length = x m


= > length of pole under ground + Length of pole in the water + length of pole above the water = x m


$= > \dfrac{x}{3} + \dfrac{x}{5} + 7 = x \\ \\ \\ \\ = > 7 = x - \frac{x}{5} - \frac{x}{3} \\ \\ \\ \\ = > 7 = \frac{15x - 3 x- 5x}{15} \\ \\ \\ \\ = > 7 \times 15 = 7x \\ \\ \\ \\ = > \frac{7 \times 15}{7} = x \\ \\ \\ \\ = > 15 = x$







So, value of variable x is 15



Total length of the pole = x m = 15 m

Answer 2

Find the fraction of the pole above water:

Fraction of the pole above water = 1 - 1/3 - 1/5 = 7/15

Form the equation:

Fraction of the pole above water = 7/15

Length of the pole above water = 7m

therefore 7/15 of the pole = 7 m

Find the length of the pole:

7/15 of the pole = 7 m

1/15 of the pole = 7 ÷ 7 = 1m

15/15 of the pole = 1 x 15 = 15 m

Answer: The pole is 15 m long.