The information about six different items used in the furniture items is as follows. Find the index number for the year 2015 with the base year 2014 and interpret it: | Items | A | B | C | D | E | F | |---|---|---|---|---|---|---| | Weight | 17 | 15 | 22 | 16 | 12 | 18 | | Price in Year 2014 ($\text{\rupee}$) | 30 | 20 | 50 | 32 | 40 | 16 | | Price in Year 2015 ($\text{\rupee}$) | 24 | 24 | 70 | 40 | 48 | 24 |

> > [!TLDR] > $I=\dfrac{\Sigma PW}{\Sigma W}=\dfrac{12380}{100}=123.8$; prices rose $23.8\%$. > > Weighted average of price relatives method, with $P=\dfrac{p_1}{p_0}\times100$: > > | Item | $W$ | $p_0$ | $p_1$ | $P=\tfrac{p_1}{p_0}\times100$ | $PW$ | > |---|---|---|---|---|---| > | A | 17 | 30 | 24 | 80 | 1360 | > | B | 15 | 20 | 24 | 120 | 1800 | > | C | 22 | 50 | 70 | 140 | 3080 | > | D | 16 | 32 | 40 | 125 | 2000 | > | E | 12 | 40 | 48 | 120 | 1440 | > | F | 18 | 16 | 24 | 150 | 2700 | > | **Total** | **100** | | | | **12380** | > …

The information about six different items used in the furniture items is as follows. Find the index number for

Question 44 of 45

The information about six different items used in the furniture items is as follows. Find the index number for the year 2015 with the base year 2014 and interpret it:

Items	A	B	C	D	E	F
Weight	17	15	22	16	12	18
Price in Year 2014 ( $\text{\text{₹}}$ )	30	20	50	32	40	16
Price in Year 2015 ( $\text{\text{₹}}$ )	24	24	70	40	48	24

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2026Subjective· 3mImportance★★★★★

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$I=\dfrac{\Sigma PW}{\Sigma W}=\dfrac{12380}{100}=123.8$ ; prices rose $23.8\%$ .

Weighted average of price relatives method, with $P=\dfrac{p_1}{p_0}\times100$ :

Item	$W$	$p_0$	$p_1$	$P=\tfrac{p_1}{p_0}\times100$	$PW$
A	17	30	24	80	1360
B	15	20	24	120	1800
C	22	50	70	140	3080
D	16	32	40	125	2000
E	12	40	48	120	1440
F	18	16	24	150	2700
Total	100				12380
…

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