#### Find the greatest integer which is such that if 7 is added to its double, the resulting number becomes greater than three times the integer.

**Solution:**

Let the greatest integer = x

According to the condition,

2x + 7 > 3x

⇒ 2x – 3x > – 7

⇒ – x > – 7

⇒ x < 7

Value of x which is greatest = 6 Ans.

#### One-third of a bamboo pole is buried in mud, one-sixth of it is in water and the part above the water is greater than or equal to 3 metres. Find the length of the shortest pole.

**Solution:**

Let the length of the shortest pole = x metre

Length of pole which is burried in mud =

Length of pole which is in the water =