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 $${\displaystyle \frac{30}{100}}\times 40.$$ 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 $${\displaystyle \frac{y}{100}}\times z.$$
So, we will first calculate 30 % of 40 using the above formula.
30 % of 40 $$={\displaystyle \frac{30}{100}}\times 40$$
Simplifying further, we get,
$$\Rightarrow {\displaystyle \frac{30\times 40}{100}}$$
$$\Rightarrow {\displaystyle \frac{1200}{100}}$$
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 $$={\displaystyle \frac{20}{100}}\times x$$
Simplifying further, we get,
$$\Rightarrow {\displaystyle \frac{20x}{100}}$$
After solving, we get,
$$20\text{ Percent of }x={\displaystyle \frac{x}{5}}......\left(ii\right)$$
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,
$$\Rightarrow 12={\displaystyle \frac{x}{5}}$$
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 $$={\displaystyle \frac{20}{100}}\times 90$$
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 $$={\displaystyle \frac{20}{100}}\times 80$$
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 $$={\displaystyle \frac{20}{100}}\times 60$$
After solving, we get,
20 % of 60 = 12
So, we get 30 % of 40 = 20 % of 60 = 12.
Hence, (c) is the correct option.