Q1: If 12% of x is equal to 6% of y, then 18% of x will be equal to how much percent of y?
Solution:
12% of x = 6% of y
x(12%) = y(6%)
Let 18% of x = a% of y
x(18%) = y(a%)
x(12%) = y(6%)
x(18%) = y(a%)
Cross multiply
x(12%) X y(a%) = x(18%) X y(6%)
12axy = 108xy
12a = 108
Dividing both sides by the coefficient of “a”
a = 108/12
a = 9%
Q2: If a number is 20% more than the other, how much percent is the second number less than the first?
Solution:
Let the smaller number be 100
The bigger number is 20% more, that is [100 + (20% of 100)]
= (100 + 20) = 120
Now, the percentage which 20 is from 120
= (20/120) X 100 = 16.67%
Q3: If A’s income is 25% less than that of B, then how much percent is B’s income more than that of A?
Solution:
Let’s assume that B makes #100
A makes 25% less than B
= [100 – (25% of 100)]
= [100 – (25)] = #75
Now, the question becomes 100 is what percent is 75?
This can be solved by putting them up in proportion
“A” makes 75
“B” makes 100
Let percentage of “B” = y
Percentage of “A” = 100
So;
75 = 100
100 = y
Cross multiply
75 x y = 100 x 100
75y = 10000
Dividing both sides by the coefficient of y.
y = (10000)/75 = 133.3%
Therefore, B’s income is (133.3 – 100)% more than A’s income
B’s income = 33.3% more
Another method is here below 👇
Q4: If the given two numbers are respectively 7% and 28% of a third number, then what percentage is the first of the second?
Solution:
Let the 3rd number be y
First number = 7y/100
Second number = 28y/100
So, percentage of the first in the second
= [(7y/100) ÷ (28y/100)] x 100
= [(7y/100) x (100/28y)] x 100
= 7/28 x 100
= 1/4 x 100 = 25%
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