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If a given number is increased by 8% of itself, then it gives the value 135. Find the actual value of given number?
(a) 112
(b) 100
(c) 125
(d) None of these
Answer
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Hint: We start solving the problem by assuming the variable for the actual number. We use the given information increasing 8% about the number to proceed through the problem. We use the fact that a% of y is defined as $\dfrac{a}{100}\times y$ to proceed further through the problem. We make necessary calculations to get the required value of ‘x’.
Complete step by step answer:
Given that we had a number and when it is increased by 8% of itself, we get the value of 135. We need to find the value of the actual number.
Let us assume the number is ‘x’ and when this is increased by 8% of itself, we get the value of 135.
So, (100% + 8%) of the value of x = 135.
Then 108% of the value of x = 135 ---(1).
We know that a% of y is defined as $\dfrac{a}{100}\times y$. We use this result in equation (1).
$\Rightarrow \dfrac{108}{100}\times x=135$.
$\Rightarrow 1.08\times x=135$.
$\Rightarrow x=\dfrac{135}{1.08}$.
x = 125.
We have found the value of ‘x’ before increasing to 125.
∴ The actual value of the given number is 125.
So, the correct answer is “Option C”.
Note: We should not multiply 108 to x i.e., $108\times x=135$, to find the value of x. We should not make any calculation mistakes while solving this problem. We can also expect problems to find the 20% of x after getting the value of x.
Complete step by step answer:
Given that we had a number and when it is increased by 8% of itself, we get the value of 135. We need to find the value of the actual number.
Let us assume the number is ‘x’ and when this is increased by 8% of itself, we get the value of 135.
So, (100% + 8%) of the value of x = 135.
Then 108% of the value of x = 135 ---(1).
We know that a% of y is defined as $\dfrac{a}{100}\times y$. We use this result in equation (1).
$\Rightarrow \dfrac{108}{100}\times x=135$.
$\Rightarrow 1.08\times x=135$.
$\Rightarrow x=\dfrac{135}{1.08}$.
x = 125.
We have found the value of ‘x’ before increasing to 125.
∴ The actual value of the given number is 125.
So, the correct answer is “Option C”.
Note: We should not multiply 108 to x i.e., $108\times x=135$, to find the value of x. We should not make any calculation mistakes while solving this problem. We can also expect problems to find the 20% of x after getting the value of x.
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