Question

When any number is divided by 12, then the dividend becomes $$\dfrac{1}{4}$$ th of the other number. By how much is the first number greater than the second number?
A. 150
B. 200
C. 300
D. Data inadequate

Answer 1

Hint: In this question it is given that any number is divided by 12, then the dividend becomes $$\dfrac{1}{4}$$ th of the other number. Then we have to find how much is the first number greater than the second number. So for this we need to consider these unknown numbers and after that the given data can form the equation. And lastly by the percentage formula we have ro find the solution,
So for this we need to know one formula which is, if p and q be two quantity then change percentage of p and q w.r.t ‘q’ is,
Change percentage = $$\dfrac{\text{change value} }{q} \times 100\%$$,
Where change value is (p-q) or (q-p) [which must be positive]

Complete step-by-step answer:
Given that, any number is divided by 12, then the dividend becomes $$\dfrac{1}{4}$$ th of the other number.
Let the first number be x and the second number be y.
Therefore, $$\dfrac{x}{12} =\dfrac{1}{4} \text{of} \ y$$
   $$\Rightarrow \dfrac{x}{12} =\dfrac{1}{4} \times y$$
   $$\Rightarrow \dfrac{x}{12} =\dfrac{y}{4}$$
   $$\Rightarrow x=3y$$

Therefore, the required percentage w.r.t ‘y’
=$$\dfrac{x-y}{y} \times 100\%$$
=$$\dfrac{3y-y}{y} \times 100\%$$
=$$\dfrac{2y}{y} \times 100\%$$
=$$2\times 100\%$$
=$$200\%$$
Hence the correct option is option B.


Note: In this question it is given that by how much is the first number greater than the second number,i.e, it is given that we have to find the change w.r.t second number (y), so that is why we divide the change by ‘y’. Also while calculating the change always subtract the smaller value from larger value.