The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. The average marks scored by a class is 72.5. Find the total number of students in the class. I. Difference between the number of boys and number of girls is 12. II. The average marks scored by the boys is 70.5. III. The average marks scored by the girls is 75.5.?

Question

The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. The average marks scored by a class is 72.5. Find the total number of students in the class. I. Difference between the number of boys and number of girls is 12. II. The average marks scored by the boys is 70.5. III. The average marks scored by the girls is 75.5.?

I & II
I & III
II & III
Any two
All three

LohaHridoy

5 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 5 : All three

Let there are ‘x’ boys and ‘y’ girls in the class

⇒ Total marks scored by class = 72.5(x + y)

Considering statement I,

Difference between number of boys and girls = 12

⇒ x - y = 12 ---- (1)

Considering statement II,

Average marks scored by boys = 70.5

⇒ Total marks scored by boys = 70.5x

Considering statement III,

Average marks scored by girls = 75.5

⇒ Total marks scored by girls = 75.5y

Using information from II and III,

Total marks scored by class = 70.5x + 75.5y

⇒ 72.5x + 72.5y = 70.5x + 75.5y

⇒ x = 3y/2

Substituting in (1),

⇒ 3y/2 - y = 12

⇒ y = 24

⇒ x = y + 12 = 24 + 12 = 36

⇒ Total no. of students in class = x + y = 36 = 24 = 60

∴ The question can be answered using all the three statements