The GATE Grind

GATE 2025 CY – Question 10

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

The number of patients per shift ($X$) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹1000$(X-0.2)$, what is the average amount (in ₹) she has earned per shift in the past 100 shifts? Note: The figure shown is representative.

Patient counts 5, 6, 7, 8 occurred in 20, 40, 30, 10 shifts respectively.
  1. 6,100
  2. 6,300
  3. 6,000
  4. 6,500 20 40 30 10 0 10 20 30 40 50 5 6 7 8 Number of shifts Number of patients per shift (X)

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 6,100

Explanation

**Mean number of patients per shift.** The chart gives 20, 40, 30 and 10 shifts for 5, 6, 7 and 8 patients respectively, a total of 100 shifts:
$$\bar X=\frac{20(5)+40(6)+30(7)+10(8)}{100}=\frac{100+240+210+80}{100}=\frac{630}{100}=6.3 .$$

**Mean earning per shift.** The amount earned is a linear function, ₹$1000(X-0.2)$, so the mean earning is the same function applied to the mean:
$$1000(6.3-0.2)=1000\times6.1=\mathbf{₹6100}.$$