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Q.

State true or false: ‘The number whose fifth part increased by 5 is equal to its fourth part diminished by 5, is 200’.


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a

True

b

False 

answer is A.

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Detailed Solution

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We are given a statement that a number whose fifth part increased by 5 is equal to its fourth part diminished by 5, is 200. We have to state if this statement is true or false.
So, assume the number to be x. Now, as per the condition, the fifth part of the number increased by 5 is equal to its fourth part diminished by 5.
This can be expressed mathematically as follows,
x 5 +5= x 4 −5   Now, to solve for x, we will take the LCM of 5 and 4 i.e., 20 and multiply each side by 20 and simplify the equation as follows,
x 5 (20)+5(20)= x 4 (20)−5(20) 4x+100=5x−100
Next, we will subtract 5x from each side of the equation and simplify as follows,
4x−5x=5x−200−5x
  −x=−200
−x −1 = −200 −1
x=200 So, the number is 200, which is the same as stated in the given statement.
Hence, the given statement is true.
So, the correct option is 1.
 
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