Find two numbers such that their mean proportion is 12 and third proportion is 768.
- A3 and 24
- B3 and 48
- C6 and 48
- D6 and 24
Solution & Step-by-step Explanation
Let the two numbers be a and b.
Mean Proportion Condition:
ab
=12⟹ab=144
Third Proportion Condition:
a
b
2
=768⟹b
2
=768a
From the first condition, we can express a as a=
b
144
. Substitute this into the second condition:
b
2
=768(
b
144
)
b
3
=768×144
b
3
=(2
8
×3)×(2
4
×3
2
)=2
12
×3
3
b=(2
12
×3
3
)
1/3
=2
4
×3=16×3=48
Now, find a:
a=
48
144
=3
Thus, the two numbers are 3 and 48.
Mean Proportion Condition:
ab
=12⟹ab=144
Third Proportion Condition:
a
b
2
=768⟹b
2
=768a
From the first condition, we can express a as a=
b
144
. Substitute this into the second condition:
b
2
=768(
b
144
)
b
3
=768×144
b
3
=(2
8
×3)×(2
4
×3
2
)=2
12
×3
3
b=(2
12
×3
3
)
1/3
=2
4
×3=16×3=48
Now, find a:
a=
48
144
=3
Thus, the two numbers are 3 and 48.