Question

In a certain examination, a total of 3768 students secured first division in the years 2006 and 2007. The number of first division in 2007 exceeded those in 2006 by 34. How many students got first division in 2006?

Answer 1

Let the number of students who got first division in the year 2006 be x.

Since, the number of first division in year 2007 exceeded those in year 2006 by 34, therefore the number of students who got the first division in year 2007 will be (x + 34).

It is given that the total number of students who got first division in years 2006 and 2007 is 3768.

According to the question,

x + (x + 34) = 3768

⇒ 2x + 34 = 3768

⇒ 2x = 3768 – 34  ...[Transposing 34 to RHS]

⇒ 2x = 3734

⇒ `(2x)/x = 3734/2`   ...[Dividing both sides by 2]

⇒ x = 1867

Hence, 1867 students got first division in year 2006.