d Arithmetic (Average Calculation)
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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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1 Comment

  1. Reply

    KPK public service commission has the word to word same syllabus for PMS as is for CSS by Federal Service Commission,
    This is great advantage for KPK candidates because whoever from KPK starts preparation for CSS or PMS is at the same also preparing for both the exams.

    In Punjab the matter is different – syllabus content is different with Urdu as additional subject!

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