Question

the difference between the squars of
two consecutive numbers
is 35. The numbers are -
(A) 14, 15 (B) 15, 16
(C)17, 18
(D) 18, 19​

Answer 1

Answer:

Let the 2 numbers be ( x - 1 ) and x

Given that, difference between the squares of the two numbers is 35.

→ x² - ( x - 1 )² = 35

→ x² - ( x² - 2x + 1 ) = 35

→ x² - x² + 2x - 1 = 35

→ 2x - 1 = 35

→ 2x = 35 + 1 = 36

→ x = 36 ÷ 2 = 18

⇒ ( x - 1 ) = 18 - 1

⇒ ( x - 1 ) = 17

Therefore the two consecutive numbers are 17 and 18.

Hence option ( C ) is the appropriate option.

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt given\begin{cases} \sf{Difference \: between \: squares \: of \: numbers = 35} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the numbers.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

Let first number be x.

Second number be (x - 1).

A.T.Q

$\tt{→ x^2 - (x - 1)^2 = 35} \\ \\\bf{We \: know \: that,} \\ \\ \Large{\boxed{\rm {(a - b)^2 = a^2 + b^2 - 2ab}}} \\ \\ \tt{→x^2 - (x^2 + 1 - 2x) = 35} \\ \\ \tt{\cancel{x^2} - \cancel{x^2} - 1 + 2x = 35} \\ \\ \tt{2x = 36} \\ \\ \tt{x = \frac{36}{2}} \\ \\ \tt{x = 18}$

• First Number = x = 18
• Second number = (x - 1) = 17

$\Large{\sf{\therefore \: Option \: C \: is \: correct}}$