2025 · Q69
If a²ˣ = b³ʸ = c⁵ᶻ and b = a²c, then which one of the following is true?
general-mental-abilityquantitative-aptitude
- A2/x + 3/y = 5/z
- B1/x − 3/(5z) = 1/(3y)
- C1/x + 1/(5z) = 1/(3y)
- D2/x − 5/z = 3/y
Explanation
Let a^(2x) = b^(3y) = c^(5z) = k. Taking logs: 2x ln a = 3y ln b = 5z ln c = ln k, so ln a = (ln k)/2x, ln b = (ln k)/3y, ln c = (ln k)/5z. From b = a^2 c, ln b = 2 ln a + ln c, i.e. (ln k)/3y = 2(ln k)/2x + (ln k)/5z. Dividing by ln k gives 1/3y = 1/x + 1/5z.