What will be the number whose fifth part increased by 30 is equal to its fourth part decreased by 30?

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1100

1200

1500

1400

answer is B.

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Detailed Solution

We have to find the number whose fifth part increased by 30 is equal to its fourth part decreased by 30.
Also, in transposition, we shift a number from one side of an equation to the other.
Suppose the number is x.

∴ x 5 + 30 = x 4 − 30

Now transposing

x 4

to LHS and 30 to RHS:

∴ x 5 − x 4 = − 30 − 30 ⇒ 4 x − 5 x 20 = − 60 ⇒ − x 20 = − 60 ⇒ x = 60 × 20 ⇒ x = 1200

So, the required number is 1200.
Therefore, option 2 is correct.

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