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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.


1. 1556
2. 1560
3. 1576
4. 1545
5.

None of the above

1 Answer

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Correct Answer - Option 2 : 1560

Calculation:

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

In 2020:

Students who appeared in exam P = 1200/5 × 4

⇒ 960

Students who appeared in exam Q = 1120 × 2 - 960 

⇒ 1280

Students who appeared in exam R = 1200

∴ Total students who appeared = 960 + 1280 + 1200

⇒ 3440

∴ Number of students cleared exam = 10% of 1120 + 20% of 1440 + 20% of 1800 + 20% of 960 + 10% of 1280 + 40% of 1200

⇒ 112 + 288 + 360 + 192 + 128 + 480

⇒ 1560

The students that cleared all three exams in these two years are 1560.

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