1.

Find three constituent whole number whose sum is more than 45 but less than 54

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Answer:

Let the three consecutive numbers be: ( x - 1 ), x, ( x + 1 )

ACCORDING to the question,

⇒ x + 1 + x + x - 1 > 45

⇒ 3x > 45

⇒ x > 15   ...( 1 )

ALSO,

⇒ x + 1 + x + x - 1 < 54

⇒ 3x < 54

⇒ x < 18 ...( 2 )

Hence x is greater than 15, x is less than 18.

So x can take two values, EITHER x is 16 or x is 17.

Case 1: x = 16

⇒ x - 1 = 16 - 1 = 15, x + 1 = 16 + 1 = 17

Hence Sum = 15 + 16 + 17 = 48 which is less than 54 and greater than 45.

Case 2: x = 17

⇒ x - 1 = 17 - 1 = 16, x + 1 = 17 + 1 = 18

Hence Sum = 16 + 17 + 18 = 51 which is less than 54 and greater than 45.

So the three numbers can be, ( 15, 16, 17 ) or ( 16, 17, 18 ).


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