Question

Comprehension

The information given below is regarding the number of students who appeared in three different exams P, Q, and R in four different years 2017, 2018, 2019, and 2020.

In 2017:

Students who appeared in exam P was twice the students who appeared in exam Q. Total students who appeared in three exams together was 3280. Students who appeared in exam Q was 80 more than students who appeared in exam R.

In 2018:

Students who appeared in exam Q were 40% more than students who appeared in exam P while students who appeared in exam R were 20% more than students who appeared in exam Q. Total students who appeared in all three exams together was 4896.

In 2019:

The ratio of students who appeared in exam P to exam Q was 7 : 9. Students who appeared in exam R was 25% more than students who appeared in exam Q. Total students who appeared in all three exams together was 4360.

In 2020:

The average of students who appeared in exams P and Q was 1120. Students who appeared in exam R was 1200. The ratio of students who appeared in exam P to exam R was 4 : 5.

What is the difference between the number of students who appeared in exams Q and R together in 2017 and the number of students who appeared in exams P and Q together in 2019?

1.  960
2.  980
3.  950
4.  970
5. None of the above

Answer 1

Correct Answer - Option 1 :  960

Calculation:

In 2017:

Let students who appeared in exam Q = y

Students who appeared in exam P = 2y 

Students who appeared in exam R = y - 80 

∴ y + 2y + y - 80 = 3280

⇒ 4y = 3360

⇒ y = 840

∴ students who appeared in exam P = 1680

∴ students who appeared in exam Q = 840

∴ students who appeared in exam R = 760

In 2019:

Let the students who appeared in exam P and Students who appeared in exam Q be 7z and 9z.

Students who appeared in exam R = 125% of 9z

⇒ 11.25z

∴ 7z + 9z + 11.25z = 4360

⇒ 27.25z = 4360

⇒ z = 160

∴ students who appeared in exam P = 1120

∴ students who appeared in exam Q = 1440

∴ students who appeared in exam R = 1800

Number of students who appeared in exams Q and R in 2017 = 840 + 760

⇒ 1600

Number of students who appeared in exams P and R in 2019 = 1120 + 1440

⇒ 2560

∴ required difference = 2560 - 1600

⇒ 960

The difference between the number of students who appeared in exams Q and R together in 2017 and the number of students who appeared in exams P and Q together in 2019 is 960