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13. statistics — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS13. statistics1 Mark
MCQ
In a city, the total income of all people with salary below $₹ 10000$ per annum is less than the total income of all people with salary above $₹ 10000$ per annum. If the salaries of people in the first group increases by $5 \%$ and the salaries of people in the second group decreases by $5 \%$, then the average income of all people
  • A
    increases
  • ✓
    decreases
  • C
    remains the same
  • D
    cannot be determined from the data
✓

Answer

Correct option: B.
decreases
b
(b)

Let total number of people whose salary less than $10000\,Rupees$ per annum $=x$ and annual salary of each person $=a$

$\therefore$ Total salary $=a x$

and total number of people whose salary more than $10000\,Rupees$ per annum $=y$ and annual salary of each person $=b$

$\therefore$ Total salary $=b x$

When $5 \%$ increase of salary of people $x$ i.e. $\quad x(a+5 \%$ of $a)=\frac{105 a x}{100}$

and $5 \%$ decrease of salary of people $y$ i.e. $y(b-5 \%$ of $b)=\frac{95 b y}{100}$

$\frac{\text { Average salary after }}{\text { Average salary before }} =\frac{105 a x+95 b y}{a x+b y}$

$=1+\frac{5}{100}\left(\frac{a x-b y}{a x+b y}\right)$

$a x-b y < 0$

$\therefore$ Average salary af ter be decreases.

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