Solutions
Given:
Money of 'A' = 20% more than Money of B and,
Money of 'C' = 20% less than Money of B.
Concept Used:
Percentage: A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the per cent sign, '%'.
If P is x per cent more than Q, then
P = Q{1 + (x/100)}
If P is x per cent less than Q, then
P = Q{1 - (x/100)}
Percentage of P more than Q
= {(P - Q)/Q} × 100%
Calculation:
Let, B have x money, then according to the question,
Money of 'A' = 20% more than Money of B
A = B{1 + (20/100)}
⇒ A = (6/5) × B ----(1)
Money of 'C' = 20% less than Money of B, i.e
C = B{1 - (20/100)}
⇒ C = (4/5) × B ......(2)
So, the amount of money of A, more than C will be
A - C = (6/5 - 4/5) × B
⇒ A - C = (2/5) × B
Percentage of money, A has more than C
{(A - C)/C} × 100%
⇒ {(2/5) × B}/{(4/5) × B} × 100%
= (1/2) × 100%
⇒ 50%
∴ A has 50% more money than C.
Alternate Method
Let, B has 100 rupees
Then, according to the question,
Money of A = 120 rupees, and
Money of C = 80 rupees
Therefore, the difference in money between A and C
= 40 rupees
Percentage of money, A have more than C = {(A - C)/C} × 100%
⇒ (40/80) × 100%
⇒ (1/2) × 100%
⇒ 50%
∴ A has 50% more money than C.