The GATE Grind

GATE 2022 AE – Question 7

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

For the past $m$ days, the average daily production at a company was 100 units per day. If today’s production of 180 units changes the average to 110 units per day, what is the value of $m$?

  1. 18
  2. 10
  3. 7
  4. 5

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Show answer and explanation

Correct answer: (C) 7

Explanation

Let the total production over the first $m$ days be $100m$ units.

**Step 1: write the new average.** After today, there are $m+1$ days and the total is $100m+180$, with average 110:
$$\frac{100m+180}{m+1}=110.$$

**Step 2: solve.**
$$100m+180=110m+110\;\Rightarrow\;70=10m\;\Rightarrow\;m=7.$$

**Check:** $7\times100+180=880$ and $880/8=110$. ✓

So $m=\mathbf{7}$.