If the numerator of a fraction is increased by 20% and the denominator is decreased by 30%, the fraction obtained is
25
39
. The original fraction is:
- A75
67
- B91
100
- C68
75
- D100
91
Solution & Step-by-step Explanation
Let the original fraction be
b
a
.
According to the question:
The numerator is increased by 20%⟹1.2a
The denominator is decreased by 30%⟹0.7b
The new fraction is:
0.7b
1.2a
=
25
39
7b
12a
=
25
39
Solving for
b
a
:
b
a
=
25
39
×
12
7
Simplifying the fraction by dividing 39 and 12 by 3:
b
a
=
25×4
13×7
=
100
91
b
a
.
According to the question:
The numerator is increased by 20%⟹1.2a
The denominator is decreased by 30%⟹0.7b
The new fraction is:
0.7b
1.2a
=
25
39
7b
12a
=
25
39
Solving for
b
a
:
b
a
=
25
39
×
12
7
Simplifying the fraction by dividing 39 and 12 by 3:
b
a
=
25×4
13×7
=
100
91