The following histogram shows the marks scored by 40 students in a test of 30 marks. A student has to score a minimum of 10 marks to pass the test.

How many students have scored less than two-third of the total marks?

The correct answer is 25.

From the histogram titled "Marks scored in 30 Marks test", we can read the number of students in each 5-mark interval:

  • Marks 0 – 5: 2 students
  • Marks 5 – 10: 8 students
  • Marks 10 – 15: 7 students
  • Marks 15 – 20: 8 students
  • Marks 20 – 25: 10 students
  • Marks 25 – 30: 5 students

Step 1: Find two-thirds of the total marks.

The total marks in the test = 30.

Two-thirds of total marks = \frac{2}{3}\times 30=20

So we need to find how many students scored less than 20 marks.

Step 2: Identify the intervals that fall below 20 marks.

All intervals strictly below 20 are:

  • 0 – 5 → 2 students
  • 5 – 10 → 8 students
  • 10 – 15 → 7 students
  • 15 – 20 → 8 students

Step 3: Add up the students in those intervals.

2+8+7+8=25

Therefore, 25 students have scored less than two-thirds (i.e., less than 20) of the total marks.