The salary of Gaganjyot is 7/6 times the salary of Hafiz and the salary of Sayed is 8/7 times the salary of Hafiz. What is the ratio of Gaganjyot's salary to Sayed's salary?

Introduction / Context:
This question examines how to combine two comparative statements that are both expressed in terms of a third person's salary. It is a classic application of ratios and fractions. The goal is to find the ratio between Gaganjyot and Sayed even though both salaries are initially given in relation to Hafiz. Converting all information to a common base (Hafiz) and then simplifying is the main technique here.

Given Data / Assumptions:

• Let Hafiz's salary be H.
• Gaganjyot's salary = (7 / 6) * H.
• Sayed's salary = (8 / 7) * H.
• We need to find the ratio of Gaganjyot's salary to Sayed's salary.

Concept / Approach:
When multiple quantities are expressed as fractions of a common quantity, we can express each explicitly and then divide one by the other to find the required ratio. Here, the ratio Gaganjyot : Sayed is equal to [(7 / 6) * H] : [(8 / 7) * H]. After cancelling H, the ratio reduces to a fraction involving only numbers. Simplifying that fraction yields the final ratio.

Step-by-Step Solution:
Assume Hafiz's salary = H.Then Gaganjyot's salary = (7 / 6) * H.Sayed's salary = (8 / 7) * H.Required ratio = Gaganjyot : Sayed = (7 / 6) * H : (8 / 7) * H.Cancel the common factor H to get (7 / 6) : (8 / 7).Write this as a single fraction: (7 / 6) / (8 / 7) = (7 / 6) * (7 / 8).Compute: (7 / 6) * (7 / 8) = 49 / 48.Therefore, Gaganjyot : Sayed = 49 : 48.

Verification / Alternative check:
Take a convenient value for H, for example H = 48.Then Gaganjyot's salary = (7 / 6) * 48 = 56.Sayed's salary = (8 / 7) * 48 ≈ 54.857, but for ratio work it is more convenient to work algebraically.Direct algebraic simplification already showed Gaganjyot : Sayed = 49 : 48, which is the simplest integer form of the ratio.

Why Other Options Are Wrong:
Options like 3 : 4 or 4 : 3 treat the multipliers 7/6 and 8/7 very roughly and ignore the actual division (7 / 6) / (8 / 7). The options 48 : 49 and 7 : 8 invert or simplify the fraction incorrectly. Only 49 : 48 exactly matches the fraction 49 / 48 obtained after proper simplification.

Common Pitfalls:
A frequent mistake is to attempt to take the ratio 7/6 : 8/7 as 7 : 8 or 6 : 7 directly without doing the correct fractional division. Some students also multiply the fractions incorrectly by adding or subtracting numerators and denominators. The safe method is to always convert a : b where a and b are fractions into a / b and then multiply by the reciprocal of b to simplify.

Final Answer:
The ratio of Gaganjyot's salary to Sayed's salary is 49 : 48.