The mean of 10 numbers is 12.5; the mean of the first six is 15 and the last fiv

Question

The mean of 10 numbers is 12.5; the mean of the first six is 15 and the last five is 10. The sixth number is

Options:

A . 15

B . 12

C . 18

D . none of these

Answer: Option A
:
A
Let the mean of the last four be

A_{2}

.
Then by the formula for combined mean,

12.5 = \frac{6 \times 15 + 4 \times A_{2}}{6 + 4}; or 125=90+4 A_{2};

∴ A_{2} = \frac{35}{4}

Let the sixth number = x; then taking the sixth number as a collection, the combined mean of this collection and the collection of the last five is 10, by question.

∴

By definition of combined mean

10 = \frac{1 \times x + 4 \times \frac{35}{4}}{1 + 4}; 50 = x + 35; ∴ x = 15

∴

sixth number = 15

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