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State true or false.

Two numbers are given such that when each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x and the second number is (40 – x), then the difference between them is 40.

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True

False

answer is B.

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Detailed Solution

We have to check if the difference between the two numbers is 40.
According to the question, the first number equals

⇒ x

and

40 − x

is the second number.
Suppose,

⇒ 40 − x > x .

Then,

40 − x + 8

= 3(x+8)

⇒ 48 − x

= 3x + 24

⇒

− x − 3 x

= 24-48

⇒

− 4 x

= -24

⇒ 4 x = 24 ⇒ x = 244 x = 6 ∴ x = 6 is one number . 40 − x is the other number . ⇒ 40 − 6 = 34

So, the difference between the numbers is:

⇒ 34 − 6 = 28

So, it can be concluded that the difference between the two numbers is 28, not 40, and thus the given statement is false.
Therefore, option 2 is correct.

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