###### Advertisements

###### Advertisements

The difference between the squares of two consecutive numbers is 31. Find the numbers.

###### Advertisements

#### Solution

Let the numbers be x and x + 1 .

According to the question,

\[(x + 1 )^2 - x^2 = 31\]

\[\text{ or }x^2 + 2x + 1 - x^2 = 31\]

\[\text{ or }2x = 31 - 1\]

\[\text{ or }x = \frac{30}{2}\]

or x = 15

Thus, the numbers are 15 and 16 .

#### APPEARS IN

#### RELATED QUESTIONS

Solve: `(9x)/(7 - 6x) = 15`

Solve: `z/(z + 15) = 4/9`

Solve: `(7y + y)/(y + 2) = (-4)/3`

Find a number whose double is 45 greater than its half.

Find a number such that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.

Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.

There are 180 multiple choice questions in a test. If a candidate gets 4 marks for every correct answer and for every unattempted or wrongly answered question one mark is deducted from the total score of correct answers. If a candidate scored 450 marks in the test, how many questions did he answer correctly?

**Solve:** `(x + 1)/(2x + 3) = 3/8`.

3 years ago, the age of a boy was y years. His age 2 years ago was (y – 2) years.

A and B are together 90 years old. Five years ago A was thrice as old as B was. Hence, the ages of A and B five years back would be (x – 5) years and (85 – x) years respectively.

`(2x - 1)/5 = (3x + 1)/3`

Divide 54 into two parts such that one part is `2/7` of the other.