Find $y$ ,if cost of living index number is $200$
Group Food Clothing Fuel and lighting House rent Miscellaneous
I $180$ $120$ $160$ $300$ $200$
W $4$ $5$ $3$ $y$ $2$

12

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Solution

The correct option is B $6$
Cost of living index number $= \frac{\sum I_{i} W_{i}}{\sum W_{i}}$
$\sum I_{i} W_{i} = 2200 + 300 y$
$\sum W_{i} = 14 + y$

$\Rightarrow$ Cost of living index number $= \frac{2200 + 300 y}{14 + y} = 200$
$\Rightarrow 2200 + 300 y = 2800 + 200 y$
$∴ y = 6$

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Similar questions

Q. For the given data calculate cost of living index number. is?

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I	$70$	$90$	$100$	$60$	$80$
W	$5$	$3$	$2$	$4$	$6$

Find the area under the frequency polygon formed using the following data

$\begin{matrix} C o s t o f l i v i n g i n d e x & N u m b e r o f w e e k s 140 - 150 & 5 150 - 160 & 10 160 - 170 & 20 170 - 180 & 9 180 - 190 & 6 190 - 200 & 2 \end{matrix}$

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Cost of living index	Number of weeks
140−150	5
150−160	10
160−170	20
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180−190	6
190−200	2

Represent the above information in the form of a histogram.

Find the mean of the following distribution.

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Q. Find the mean daily wages

Daily wages	No. of workers
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Use appropriate method.

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Find y,if cost of living index number is 200GroupFoodClothingFuel and lightingHouse rentMiscellaneousI180120160300200W453y2

The correct option is B 6Cost of living index number =∑IiWi∑Wi∑IiWi=2200+300y∑Wi=14+y⇒ Cost of living index number =2200+300y14+y=200⇒2200+300y=2800+200y∴y=6

Find $y$ ,if cost of living index number is $200$
Group Food Clothing Fuel and lighting House rent Miscellaneous
I $180$ $120$ $160$ $300$ $200$
W $4$ $5$ $3$ $y$ $2$

The correct option is B $6$
Cost of living index number $= \frac{\sum I_{i} W_{i}}{\sum W_{i}}$
$\sum I_{i} W_{i} = 2200 + 300 y$
$\sum W_{i} = 14 + y$

$\Rightarrow$ Cost of living index number $= \frac{2200 + 300 y}{14 + y} = 200$
$\Rightarrow 2200 + 300 y = 2800 + 200 y$
$∴ y = 6$