Question:
he trend line for the sales (in lakhs) is given by \(y_c=84+12(x-2017).\) The estimated sale for theyear \(2024 \) is :
he trend line for the sales (in lakhs) is given by \(y_c=84+12(x-2017).\) The estimated sale for theyear \(2024 \) is :
Updated On: May 12, 2025
- \(₹ 84\) lakh
- \(₹ 96\) lakh
- \(₹ 156\) lakh
- \(₹ 168\) lakh
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The Correct Option is D
Solution and Explanation
We are given a trend line equation for estimating sales over the years. The equation is:
yₚ = 84 + 12(x - 2017), where:
- yₚ is the estimated sales in lakhs
- x is the year
To find the estimated sales for the year 2024, substitute x = 2024 into the equation:
yₚ = 84 + 12(2024 - 2017)
= 84 + 12 × 7
= 84 + 84
= 168
Hence, based on the given linear trend, the estimated sales in the year 2024 is ₹168 lakh.
This means the model predicts a steady increase in sales of ₹12 lakh every year after 2017, and over 7 years (from 2017 to 2024), the increase is ₹84 lakh, which when added to the base value of ₹84 lakh gives ₹168 lakh.
yₚ = 84 + 12(x - 2017), where:
- yₚ is the estimated sales in lakhs
- x is the year
To find the estimated sales for the year 2024, substitute x = 2024 into the equation:
yₚ = 84 + 12(2024 - 2017)
= 84 + 12 × 7
= 84 + 84
= 168
Hence, based on the given linear trend, the estimated sales in the year 2024 is ₹168 lakh.
This means the model predicts a steady increase in sales of ₹12 lakh every year after 2017, and over 7 years (from 2017 to 2024), the increase is ₹84 lakh, which when added to the base value of ₹84 lakh gives ₹168 lakh.
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