a and b are two numbers such that their mean proportion is 6 and third proportion is 48. What is the value of a and b?
Answer & explanation
Correct answer: option 2
Mean proportional = 6
√ab = 6,
⇒ ab = 36 ..(1.)
Third proportional = 48
⇒ 48a = \( {b }^{2 } \) ..(2.)
⇒ From eq. (1.) a = \(\frac{36}{b}\) and put into (2.)
⇒ \( {b }^{3 } \) = 48 x 36
⇒ \( {b }^{3 } \) = 1728
⇒ b = 12.
⇒ Putting in (1.)
⇒ a = \(\frac{36}{12}\)
⇒ a = 3.
Therefore, a and b are 3 and 12 respectively.