If 3ᵃ = 27ᵇ = 81ᶜ and abc = 144, then the value of 12(1/a + 1/2b + 1/5c) is :

If 3ᵃ = 27ᵇ = 81ᶜ and abc = 144, then the value of 12(1/a…

If 3^a = 27^b = 81^c and abc = 144, then the value of 12(1/a + 1/2b + 1/5c) is :

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e 33/10

Explanation:

3^a = 27^b = 81^c

3^a = 3^3b = 3^4c

a = 3b = 4c

abc = 144

4c × 4c/3 × c = 144

c³ = 27

c = 3

12(1/a + 1/2b + 1/5c)

12(1/4c + 1/(8c/3) + 1/5c)

= 12(33/40c)

= 12 × 33/(40 × 3)) = 33/10