Question

What is the number whose 20 % is 30 % of 40?
(a) 90
(b) 80
(c) 60
(d) 50

Answer 1

Hint: We have to find a number whose 20 % is the same as 30 % of 40. We will first assume that the required number is x, then we will find 30 % of 40 by \[\dfrac{30}{100}\times 40.\] Similarly, we will solve the term 20 % of x. When we get these two values, we will compare them to find the value of x.

Complete step-by-step answer:
We are asked to find a number whose 20 % is 30 % of 40. We will start by assuming the required number be x. Now, we know the formula for percentage, i.e. y % of z is given as \[\dfrac{y}{100}\times z.\]
So, we will first calculate 30 % of 40 using the above formula.
30 % of 40 \[=\dfrac{30}{100}\times 40\]
Simplifying further, we get,
\[\Rightarrow \dfrac{30\times 40}{100}\]
\[\Rightarrow \dfrac{1200}{100}\]
After solving, we get,
30 % of 40 = 12…..(i)
Now using the same formula, we will find 20 % of our required number, i.e. x. So, we can write,
20 % of x \[=\dfrac{20}{100}\times x\]
Simplifying further, we get,
\[\Rightarrow \dfrac{20x}{100}\]
After solving, we get,
\[20\text{ Percent of }x=\dfrac{x}{5}......\left( ii \right)\]
Now we are given that 20 % of the number is the same as 30 % of 40. So, we will compare (i) and (ii).
30 % of 40 = 20 % of x
From (i) and (ii), we get,
\[\Rightarrow 12=\dfrac{x}{5}\]
Now, cross – multiplying, we get,
\[12\times 5=x\times 1\]
So, solving for x, we get,
\[x=60\]
So, our required answer is 60.
So, the correct answer is “Option C”.

Note: We can also use an alternate method where we will check each one of the options until we find the right option.
Now, as from (i), we have 30 % of 40 as 12, we will assume each of the options as our required number and check.
(a) Let our required number be 90
20 % of 90 \[=\dfrac{20}{100}\times 90\]
After solving, we get,
20 % of 90 = 18
Both are not equal. Hence, (a) is an incorrect option.
(b) Let our required number be 80
20 % of 80 \[=\dfrac{20}{100}\times 80\]
After solving, we get,
20 % of 80 = 16
Both are not equal. Hence, (b) is an incorrect option.
(c) Let our required number be 60
20 % of 60 \[=\dfrac{20}{100}\times 60\]
After solving, we get,
20 % of 60 = 12
So, we get 30 % of 40 = 20 % of 60 = 12.
Hence, (c) is the correct option.