Question

If square of a natural number diminished by 75 is equal to 10 times of that number, then the number is
(A) 15
(B) 18
(C) 25
(D) 31

Answer 1

Step-by-step explanation:

Let the required number be x.

According to the question,

x²-75= 10(x)

⇒x²−75=10x

⇒x²−10x-75

⇒x²−15x+5x-75

⇒x(x-15)+5(x-15)

⇒(x-15) and (x+5)

⇒x=15,x= -5

⇒x= -5is not a natural number so it is rejected.)

Hence, the required number is 15

Answer 2

Given : square of a natural number diminished by 75 is equal to 10 times of that number,

To Find : the number is​

(A) 15

(B) 18

(C) 25

(D) 31

Solution:

Let say natural number = n

square of a natural number = n²

diminished by 75  = n² - 75

10 times of that number, =  10n

Equate both

=>   n² - 75 = 10n

=> n² - 10n - 75 = 0

=> n² - 15n + 5n - 75 = 0

=> (n - 15)(n + 5)  = 0

=> n = 15 , n  =  - 5

n is a natural number hence must be a +ve integer  so  n can not be - 5

so n = 15

Verification :

15² = 225

225 - 75 = 150

15 * 10  = 150

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