The product of two consecutive natural numbers is 600. The numbers are

1.	The product of two consecutive natural numbers is 600. The numbers are ……………A) 35, 36 B) 16, 25 C) 26, 25 D) 24, 25
Answer» Correct option is (D) 24, 25 Let x & x+1 are two consecutive natural numbers whose product is 600. \(\therefore\) x (x+1) = 600 \(\Rightarrow x^2+x-600=0\) \(\Rightarrow x^2+25x-24x-600=0\) \(\Rightarrow x(x+25)-24(x+25)=0\) \(\Rightarrow(x+25)(x-24)=0\) \(\Rightarrow\) x+25 = 0 or x - 24 = 0 \(\Rightarrow\) x = -25 or x = 24 \(\therefore\) x = 24 \((\because\) x is a natural number, therefore \(x\neq-25)\) \(\Rightarrow\) x+1 = 25 Hence, required natural numbers are 24, 25. Correct option is D) 24, 25

The product of two consecutive natural numbers is 600. The numbers are ……………A) 35, 36 B) 16, 25 C) 26, 25 D) 24, 25

Answer»

Correct option is (D) 24, 25

Let x & x+1 are two consecutive natural numbers whose product is 600.

\(\therefore\) x (x+1) = 600

\(\Rightarrow x^2+x-600=0\)

\(\Rightarrow x^2+25x-24x-600=0\)

\(\Rightarrow x(x+25)-24(x+25)=0\)

\(\Rightarrow(x+25)(x-24)=0\)

\(\Rightarrow\) x+25 = 0 or x - 24 = 0

\(\Rightarrow\) x = -25 or x = 24

\(\therefore\) x = 24 \((\because\) x is a natural number, therefore \(x\neq-25)\)

\(\Rightarrow\) x+1 = 25

Hence, required natural numbers are 24, 25.

Correct option is D) 24, 25