Download App

Question Bank [2022] — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Question Bank [2022]4 Marks
Question
Calculate Walsh’s price Index Number for the following data.
Commodity Base Year Current Year
Price Quantity Price Quantity
I 10 12 40 3
II 20 2 25 8
III 30 3 50 27
IV 60 9 90 36
✓

Answer

Construct the following table:
Commodity Base
Year		 Current
Year		 $\sqrt{ q _1 q _1}$ $p _0 \sqrt{ q _0 q _1}$ $p_1 \sqrt{q_0 q_1}$
$p_0$ $q_0$ $p_1$ $q_1$
I 10 12 40 3 6 60 240
II 20 2 25 8 4 80 100
III 30 3 50 27 9 270 450
IV 60 9 90 36 18 1080 1620
Total – – – – – 1490 2410

From the table, $\sum p _0 \sqrt{ q _0 q _1}=1490, \sum p _1 \sqrt{ q _0 q _1}=2410$

Walsh's Price Index Number:
$ P_{01}(W)=\frac{\sum p_1 \sqrt{q_0 q_1}}{\sum p_0 \sqrt{q_0 q_1}} \times 100$
$=\frac{2410}{1490} \times 100$
$=161.74 $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(4 Marks)" from Question Bank [2022]→Question Bank [2022] — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

The equations of two regression lines are $10 x-4 y=80$ and $10 y-9 x=-40$ Find:
(i) $\bar{x}$ and $y$
(ii) $b_{y x}$ and $b_{x y}$
(iii) If $\operatorname{var}(Y)=36$, obtain $\operatorname{var}(X)$
(iv) $\mathrm{r}$
→
The following table shows the production of gasoline in U.S.A. for the years 1962 to 1976.
Year19621963196419651966196719681969
Production
(million barrels)		00112345
Year1970197119721973197419751976
Production
(million barrels)		67898910
a. Obtain trend values for the above data using 5-yearly moving averages.
b. Plot the original time series and trend values obtained above on the same graph.
→
The probability distribution of a discrete r.v.X is as follows.
x 1 2 3 4 5 6
P(X = x) k 2k 3k 4k 5k 6k
Complete the following activity.
Solution: Since $\sum p_i=1$
$P(X \geq 3)=\square-\square-\square=\square$
→
A trader offers a 25% discount on the catalogue price of the radio and yet makes a 20% profit. If he gains $\text{₹}$ 160 per radio, what must be the catalogue price of the radio?
→
If $X$ follows Poisson distribution such that $P(X=1)=0.4$ and $P(X=2)=0.2$, using the following activity find the value of $m$.
Solution: $X$ : Follows Poisson distribution
$ \therefore P ( X )=\frac{ e ^{- m } m ^x}{x !}, P ( X =1)=0.4 \text { and } P ( X =2)=0.2$
$\therefore P ( X =1)=\square P ( X =2) .$
$\frac{ e ^{- m } m ^x}{1 !}=\square \frac{ e ^{- m } m ^2}{2 !},$
$e ^{- m }=\square e ^{- m } \frac{ m }{2}, m \neq 0$
$\therefore m =\square $
→
Find the general solution of the equation $\frac{ d y}{ d x}-y=2 x$.
Solution: The equation $\frac{ d y}{ d x}-y=2 x$
is of the form $\frac{ d y}{ d x}+ P y= Q$
where $P =\square$ and $Q =\square$
$\therefore \text { I.F. }= e ^{\int- d x}= e ^{- x }$
$\therefore$ the solution of the linear differential equation is
$ ye ^{- x }=\int 2 x \cdot e ^{-x} d x+ c$
$\therefore ye ^{- x }=2 \int x \cdot e ^{-x} d x+ c$
$=2\left\{x \int e ^{-x} d x-\int \square d x \cdot \frac{ d }{ d x} \square d x\right\}+ c$
$=2\left\{x \frac{ e ^{-x}}{-1}-\int \frac{ e ^{-x}}{-1} \cdot 1 d x\right\}+ c$
$\therefore ye ^{- x }=-2 x \cdot e ^{-x}+2 \int e ^{-x} d x+ c$
$\therefore e ^{- x } y =-2 x \cdot e ^{-x}+2 \square+ c $
$\therefore y+\square+\square= ce ^{ x }$ is the required general solution of the given differential equation
→
Evaluate $\int_1^3 x^2 \cdot \log x \ d x$
→
A company manufactures two types of ladies dresses C and D. The raw material and labour available per day is given in the table.

Resources Dress C(x) Dress D(y) Max. availability
Raw material 5 4 60
Labour 5 3 50

P is the profit, if P = 50x + 100y, solve this LPP to find x and y to get the maximum profit

→
The age in years of 7 young couples is given below. Calculate husband’s age when wife’s age is 38 years.
Husband (x) 21 25 26 24 22 30 20
Wife (y) 19 20 24 20 22 24 18
→
$\int \frac{3 e ^{2 t }+5}{4 e ^{2 t }-5} dt$
→