Question

Assume there are four families in a country. The average per capita income of
these families is Rs 5000. If the income of three families is Rs 4000, Rs 7000
and Rs 3000 respectively, what is the income of the fourth family?​

Answer 1

$\sf \blue { \underline { \sf ✯Given :- }}$

• The average income of the four families₹5,000.
• The individual income of these families are ₹4,000, ₹7,000, and ₹3000 respectively.

$\sf \pink { \underline { \sf ✯ To \: find :- }}$

• The income of the fourth family = ??

$\sf \green { \underline { \sf ✯Solution :- }}$

• Here, the average income of four families are given in a country. To find the income of fourth family apply the formula of average.
• So, let's assume that fourth family's income is ₹x.

${ \fcolorbox{blue}{orange}{\bf \: Average}} : - \\ = \bf{ \boxed{ \bf \frac{Total \: frequency(sum \: of \: income\: of \: four \: families)}{Total \: no. \: of \: frequency(no. \: of \: families )}}}$

$\bf \implies \: 5000 = \frac{4000 + 7000 +3000 + x }{4} \\ \bf \implies \: 5000 = \frac{14000 + x}{4} \\ \bf \implies \: 5000 \times 4 = 14000 + x \\ \bf \implies \: 20000 = 14000 + x \: \\ \bf \implies \: x = 20000 - 14000 \\ \bf \therefore \: {\purple \bigstar{\underline{\boxed{ \bf x = ₹6000}}}}{\purple \bigstar}$

$\bf \therefore \: income \: of \: fourth \: family \: = ₹6000$

$\sf \purple { \underline { \sf ✯Verification :- }}$

• In the question it is told that the average is ₹5000.

• To verify it, the average must be equal after putting the value of x in the formula of average i.e., income of fourth family.

Now,

L.H.S = R.H.S

$\tt \implies \: 5000 = \frac{4000 + 7000 + 3000 + x}{4} \\ \bf (putting \: the \: value \: of \: x) \\ \tt \implies \: 5000 = \frac{14000 + 6000}{4} \\ \tt \implies \: 5000 \times 4 = 2000 \\ \bf \implies \: 2000 = 2000 \\ \bf \therefore{ \underline{ \boxed{ \bf\: LHS \: = RHS \: }}}$

$\sf { \underline{ \green{ ✧Hence, \purple V \red e \orange r \pink f \blue i \green e \red d }}}$

Answer 2

Answer:

your answer is Rs. 6,000.

Explanation:

Per capita income is the total income of the country/state divided by the number of people in that country/state.

Here a total of four families. The average per capita income (5000) is equal to (4000+7000+3000+x) / 4

Income of fourth family is Rs. 20,000 - Rs. 14,000= Rs.6,000

Hope it helps you

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