Question

The income of ‘A’ is 20% higher than that of ‘B’. The income of ‘B’ is 25% less than of ‘C’. What percent less is A’s income from C’s income?
A
7%
B
8%
C
10%
D
12.5%

Answer 1

Answer:

Easy method.

Let C's income be Rs. 100

Then according to question, we have

B's income = Rs. 75

Then A's income =120% of Rs. 75= Rs. 90

Therefore, A's income is 10% less than C.

Hard method.

Let income of A be a, income of B be b and income of C be c.

It is given that income of A is 20% higher than that of B. So, the income A is income of B added with 20% income of B. so we can write,

⇒a=b+20%b

We can write the percentage as fraction. So, we get,

⇒a=b+20/100b

On taking the LCM, we get,

⇒a=100+20/100b

So, we have,

⇒a=120/100b

On cancelling the zeros in the numerator and denominator, we get,

⇒a=12/10b … (1)

It is given that income of B is 25% less than that of C. So, the income B is income of C minus 25% of the income of C. so we can write,

⇒b=c−25%c

We can write the percentage as fraction. So, we get,

⇒b=c−25/100c

On taking the LCM, we get,

⇒b=100−25/100c

So, we have,

⇒b=75/100c … (2)

Now we can substitute equation (2) in (1).

⇒a=12/10×75/100c

On simplification, we get,

⇒a=900/1000c

We can make the denominator to 100.

⇒a=90/100c

As we need to find how much percentage less is a from c, we can write the equation as,

$\huge⇒a=c− \frac{10}{100}$

Now we write the fraction as percentage,

⇒a=c−10%c

From the equation, we can say that a is 10% less than c.

So, A’s income is 10% less than C’s income.

Therefore, the required solution is 10%

Option C is correct. 10%