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Question:

f Year on Year (YoY) Growth is  

$\left\{\frac{\mathrm{Current} \mathrm{Year} \mathrm{Sales}-\mathrm{Previous} \mathrm{Year} \mathrm{Sales}}{\mathrm{Previous} \mathrm{Year} \mathrm{Sales}}\right\}$

then the YoY growth of combined sales of all products has suffered maximum decline in which year?

Explanation:

​​​​​​​The first table gives the difference between the average sales of various products over seven years.
e.g. A – B = 214.29 crores
Hence, total difference between A and B over the seven year period is:
A – B = 214.29 × 7 = 1500 crores
Similarly,
C – A = 900 cr, A – D = 1000 cr, A – E = 300 cr, C – B = 2400 cr, D – B = 500 cr, E – B
= 1200 cr, C – D = 1900 cr, C – E = 1200 cr,
E – D = 700 cr
Let the sales of A in 2013 be a(‘000s), C in 2010 be c(‘000s) and D in 2012 be d(‘000s).
The total sales, by volume, of each product are:
A = (6800 + a) × 10³
B = 5800 × 10³
C = (7400 + c) × 10³
D = (5700 + d) × 10³
E = 7000 × 10³
Hence, difference between number of units sold of B and E = 1200 × 10³
Assuming that each product is sold at the same cost in each year,
Cost per product = (1200 cr)/(1200 thousand) = (1200 × 10⁷)/ (1200 × 10³)
= 10000
∴ Total sales of B over the given period = 5800 × 10³ × 10000 = 5800 × 10⁷ = 5800 crores
Similarly, total sales of E over the given period = 7000 × 10³ × 10000 = 7000 × 10⁷ = 7000 crores
Using these values in the equations above, A = 7300 crores, C = 8200 crores, D
= 6300 crores
Also, total sales of A = (6800 + a) × 10³ × 10000 = (6800 + a) × 10⁷
= (6800 + a) crores

The same concept can be used for this question.

The values for 2010, 2011, 2012 and 2013 were already known.

Based on the options, find the values for 2009, 2014 and 2015.

2009: 1200 + 300 + 1500 + 600 + 1300

= 4900

2014: 1800 + 700 + 1200 + 900 + 1300

= 5900

2015: 1300 + 1600 + 1000 + 1800 + 300

= 6000

Since the sales increase from 2014 to 2015, option 4 can be directly eliminates as we need to find % decline.

For the other three values, it can be observed that the maximum % decline is in 2011.

Hence, option (c).