Given:
Total number of candidates appearing for the interview = 200
Number of candidates have scored more than 60% marks in their graduation = 50
Number of candidates scored more than 60% marks in both 12th standard and 10th standard = 90
Number of candidates scored more than 60% marks in 10th standard = 120
Number of candidates scored less than 60% marks at all the three stages – 10th standard, 12th standard, and graduation = 0
Concept Used:
Use of Venn diagrams.
Calculation:
The given conditions can be represented as Venn diagram as follows:
Here, a = Number of candidates scored more than 60% marks only in 10th standard,
b = Number of candidates scored more than 60% marks in both 10th standard and 12th standard,
c = Number of candidates scored more than 60% marks only in 12th standard,
d = Number of candidates scored more than 60% marks in both 10th standard and graduation,
e = Number of candidates scored more than 60% marks in 10th standard, 12th standard and graduation,
f = Number of candidates scored more than 60% marks in both 12th standard and graduation,
g = Number of candidates scored more than 60% marks only in graduation.
To obtain the sum of the total number of candidates, who got more than 60% marks in 10th standard only and those who got more than 60% marks in 12th standard only; we need to calculate the value of (a + c).
From the given conditions,
a + b + c + d + e + f + g = 200 ….(i)
d + e + f + g = 50 ….(ii)
On subtracting the values of equation (ii) from the value of equation (i), we get
a + b + c + d + e + f + g – (d + e + f + g) = 200 - 50
⇒ a + b + c = 150
∴ The total number of candidates, who were not able to score more than 60% in graduation; is 150
Confusion Point:
We need to take note of the fact that we are asked about "the total number of candidates who were not able to score more than 60% in graduation" and not "the total number of candidates who were not able to score more than 60% in graduation only". If the latter was asked, the answer would have simply been the value of (200 - g), and not the value of (a + b + c).