# Arithmetic MCQ 5 (Average Calculation)

MCQ 5 :The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is_____________?

a) 11.0                 b) 11.3                c) 11.4                  d) 11.5

Solution:

We know that;

$Average = \frac{Sum Of Terms}{Number of Terms}$

Let the numbers are;

x1, x2, x3, x4, x5, x6, x7, x8, x9, x10  and x11

It is given that their average is 10.9 i-e

$10.9 = \frac{x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11}{11}$

From this we get; (scroll aside)

$x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11=10.9\times11=119.9——-(1$

Now we are also given that average of first six numbers x1, x2, x3, x4, x5, x6 is 10.6, so

In the same way as above

$10.5 = \frac{x1+ x2+ x3+ x4+ x5+ x6}{6}$

From this we get;

$x1+ x2+ x3+ x4+ x5+ x6=10.5\times6=63 ——-(2$

This gives;

$x1+ x2+ x3+ x4+ x5 = 63- x6——-(A$

Also given that average of last six numbers is 11.4, we get;

$11.4 = \frac{x6+ x7+ x8+ x9+ x10+ x11}{6}$

From this we get;

$x6+ x7+ x8+ x9+ x10+ x11=11.4\times6=68.4——–(3$

This gives;

$x7+ x8+ x9+ x10+ x11 = 68.4-x6——(B$

Putting values in eq 1 from eq A and B

$63- x6+ x6+ 68.4-x6=10.9\times11=119.9$

This gives;

$63+ 68.4-x6=119.9$

$x6=131.4-119.9=11.5.5$

So,

Sixth number x6 is 11.5

option d is correct

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