If decreasing 90 by k% gives the same result as increasing 60 by k%, then k% of 120 is how much percent of [(k+20)% of 150]?
- A76.42
- B40
- C60
- D45
Solution & Step-by-step Explanation
According to the problem statement:
90×(1−
100
k
)=60×(1+
100
k
)
Divide both sides by 30:
3×(1−
100
k
)=2×(1+
100
k
)
3−
100
3k
=2+
100
2k
3−2=
100
2k
+
100
3k
1=
100
5k
k=
5
100
=20
Now find the two required values:
k% of 120=20% of 120=
100
20
×120=24
(k+20)% of 150=(20+20)% of 150=40% of 150=
100
40
×150=60
We need to find what percent 24 is of 60:
Required Percentage=(
60
24
)×100=
5
2
×100=40%
90×(1−
100
k
)=60×(1+
100
k
)
Divide both sides by 30:
3×(1−
100
k
)=2×(1+
100
k
)
3−
100
3k
=2+
100
2k
3−2=
100
2k
+
100
3k
1=
100
5k
k=
5
100
=20
Now find the two required values:
k% of 120=20% of 120=
100
20
×120=24
(k+20)% of 150=(20+20)% of 150=40% of 150=
100
40
×150=60
We need to find what percent 24 is of 60:
Required Percentage=(
60
24
)×100=
5
2
×100=40%