Question

Which of the following is wrong?
\[\left( a \right)\sqrt{225}+625=80\text{ percent of }1200-320\]
\[\left( b \right)5\dfrac{1}{2}\text{ of }50\text{ percent}=2.75\]
\[\left( c \right)25\text{ percent of }50\text{ percent}=0.125\]
(d) 150 grams is 20 percent of a kg

Answer 1

Hint: We are asked to find the wrong option. We will check each of the following options, the option in which the right side is not matching with the left side will be considered as the wrong answer.

Complete answer:
Here, we have four options out of which some are incorrect and some are correct. So, we are going to look for the incorrect option. We will check each option one by one.
\[\left( a \right)\sqrt{225}+625=80\text{ percent of }1200-320\]
Consider the left-hand side.
\[\sqrt{225}+625\]
As, \[\sqrt{225}=15,\] so we can write as
\[\Rightarrow \sqrt{225}+625=15+625\]
\[\Rightarrow \sqrt{225}+625=640\]
So, we get \[\sqrt{225}+625=640.\]
Now, consider the right side.
80 percent of 1200 – 320
Here ‘of’ implies multiplication. So, we get,
\[\Rightarrow 80\text{ percent of }1200-320=\dfrac{80}{100}\times 1200-320\]
Simplifying, we get,
\[\Rightarrow 80\text{ percent of }1200-320=\dfrac{80\times 1200}{100}-320\]
\[\Rightarrow 80\text{ percent of }1200-320=80\times 120-320\]
So, we get,
\[\Rightarrow 80\text{ percent of }1200-320=960-320\]
\[\Rightarrow 80\text{ percent of }1200-320=640\]
So, we get,
Left side = Right Side
Therefore, option (a) is the correct option.
\[\left( b \right)5\dfrac{1}{2}\text{ of }50\text{ percent}=2.75\]
Consider the left side.
\[5\dfrac{1}{2}\text{ of }50\text{ percent}\]
Changing into a simple fraction, we get,
\[\Rightarrow 5\dfrac{1}{2}\text{ of }50\text{ percent}=\dfrac{11}{2}\text{of }50\text{ percent}\]
Simplifying we get,
\[\Rightarrow 5\dfrac{1}{2}\text{ of }50\text{ percent}=\dfrac{11}{2}\times \dfrac{50}{100}\]
\[\Rightarrow 5\dfrac{1}{2}\text{ of }50\text{ percent}=\dfrac{11}{4}\]
So, we get,
\[\Rightarrow 5\dfrac{1}{2}\text{ of }50\text{ percent}=2.75\]
Therefore, the left side is equal to the right side.
Therefore, option (b) is also the correct option.
\[\left( c \right)25\text{ percent of }50\text{ percent}=0.125\]
Consider the left side.
25 of 50 percent
On simplifying, we get,
\[\Rightarrow 25\text{ percent of }50\text{ percent}=\dfrac{25\times 50}{100\times 100}\]
\[\Rightarrow 25\text{ percent of }50\text{ percent}=\dfrac{1250}{1000}\]
\[\Rightarrow 25\text{ percent of }50\text{ percent}=0.125\]
So, clearly we get, the left side is the same as the right side.
Therefore, option (c) is also the correct option.
(d) 150 grams is 20 percent of a kg
Consider 20 percent of a kg
As we know that 1 kg has 1000 grams, so,
20 percent of a kg = 20 percent of 1000 grams
On simplifying, we get,
\[\Rightarrow 20\text{ percent of a kg}=\dfrac{20}{100}\times 1000\]
\[\Rightarrow 20\text{ percent of a kg}=\dfrac{20000}{100}\]
\[\Rightarrow 20\text{ percent of a kg}=200\]
So, 20 percent of a kg is 200.
So, 200 is not matching with 150. Therefore, option (d) is not the correct option.

Hence, option (d) is our required answer.

Note:
Students must note that while solving always remember to change the percentage into fractions where we divide the term by 100 like 25 percent is written as \[\dfrac{25}{100}.\] And the application of ‘of’ is to multiply the terms and lastly we always should remember to follow BODMAS rule.