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### Question

Mr. X travels 8 km at a speed of 23 km/h, and 16 km at a speed of 17 km/h. What is the average speed during the entire journey?

**A**

19 km/h.

**B**

20 km/h.

**C**

18 km/h.

**D**

22 km/h.

**Soln.**

**Ans: a**

We shall use the alligation formula. If a sample n_{1} has an average property of A_{1}, and another sample n_{2} has an average property of A_{2}, then the average property of the mixture, A, is determined by the alligation formula as: n_{1}(A - A_{1}) = n_{2}(A_{2} - A). Putting A_{2} = 17, A_{1} = 23, n1 = 8, n2 = 16, we have 8 × (A - 23) = 16 × (17 - A), from where we get A = 19 km/h. *The "property" in the alligation formula could be speed, weight, price, etc.,*