If 20% of a is added to 40% of b, the answer is 50% of b. What percentage of b is a
Answers
'a' is 50 percent of 'b'.
• 20 % of 'a' can be written as (20 / 100) × a
40 % of 'b' can be written as (40 / 100) × b
50 % of 'b' can be written as (50 / 100) × b
• According to the question,
20 % of a + 40 % of b = 50 % of b
=> (20 / 100) × a + (40 / 100) × b = (50 / 100) × b
=> (20a / 100) + (40b / 100) = 50b / 100
=> (20a + 40b) / 100 = 50b / 100
On cross-multiplication,
=> 20a + 40b = (50b × 100) / 100
=> 20a + 40b = 50b
=> 20a = 50b - 40b
=> 20a = 10b
=> a = 10b / 20
=> a = b / 2 -(i)
• Now, the percentage of one number with respect to another is given by the formula :
( Number 1 / Number 2 ) × 100 %
• Therefore, the percentage of 'a' with respect to 'b' is given as :
(a / b) × 100 %
Substituting a with b / 2 from eq. (i), we get,
[ (b / 2) / b ] × 100 %
= [ (b / 2) × (1 / b) ] × 100 %
= [ (b × 1) / (2 × b) ] × 100 %
= (b / 2b) × 100 %
= 50 %
∴ a is 50 % of b.