Questions & Answers

Question

Answers

(a) 90

(b) 80

(c) 60

(d) 50

Answer
Verified

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.

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.