Question

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

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.

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.