The monthly distribution of $9$ Watt LED bulbs sold by two firms $X$ and $Y$ from January to June $2018$ is shown in the pie-chart and the corresponding table. If the total number of LED bulbs sold by the two firms during April-June $2018$ is $50000$, then the number of LED bulbs sold by the firm $Y$ during April-June $2018$ is ________.

Percentage of $9$ Watt LED bulbs sold  by the firms $X$ and $Y$ from January $2018$ to June,$2018$

$$\begin{array}{|c|c|} \hline {} & \text{ Ratio of LED bulbs} \\ \text{Month} & \text{ sold by two firms} \\ & (X:Y) \\ \hline \text{January} & 7:8 \\ \hline \text{February} & 2:3 \\ \hline \text{March} & 2:1 \\ \hline \text{April} & 3:2 \\ \hline \text{May} & 1:4 \\ \hline \text{June} & 9:11 \\ \hline \end{array}$$

1. $11250$
2. $9750$
3. $8750$
4. $8250$

We can find the number of LED bulbs sold by $Y$ during April – June $2018$ by adding up the monthly units sold.

• LED bulbs sold in April by $Y = \dfrac{2}{5} \times 15\% = 6\%$
• LED bulbs sold in May by $Y = \dfrac{4}{5} \times 10\% = 8\%$
• LED bulbs sold in June by $Y = \dfrac{11}{20} \times 10\% = 5.5\%$

Total LED bulbs sold by $Y$ during April-June $= (6 + 8 + 5.5)\% = 19.5\%.$

The total number of LED bulbs sold by the two firms during April-June $= 50000 (15\%+10\%+10\% = 35\%).$

• $35\% \longrightarrow 50000$
• $19.5\% \longrightarrow \left(\dfrac{50000}{35} \right) \times 19.5 = 27857.1428.$
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