### Study the following information carefully and answer the questions given below :

There are a certain number of students who appeared exams conducted in different subjects UPSC , BANK and SSC . All of them have cleared at least one exam . 39.4% students cleared UPSC exam , 41.4% students cleared BANK exam and 53.6% students cleared SSC . 8% students cleared only UPSC and BANK , 7% students cleared only BANK and SSC exam and 9.8% students cleared only UPSC and SSC Exams . If total number of students in the group is 500.**1. How many students cleared all 3 examinations ?**

1.16

2.14

3.32

4.48

5.36

**2.What is the percentage of students who cleared the only UPSC examination ?**

1.14.6%

2.16.8%

3.18%

4.24%

5.12.4%

**3.How many students are there who cleared at least two examination ?**

1.142

2.136

3.132

4.128

5.148

**4.What is the % of students who cleared the examination BANK but couldn't SSC ?**

1.29.6%

2.28.4%

3.27%

4.21.6%

5.23.4%

**5.How many students are there who cleared at most one exam conducted by these three exams ?**

1.204

2.168

3.308

4.352

5.376

### Solutions and Answers :

**Solution :**

No.of students cleared UPSC = 197

No.of students cleared BANK = 207

No.of students cleared SSC =268

No.of students only cleared UPSC = X

No.of students only cleared BANK = Y

No.of students only cleared SSC = Z

No.of students cleared all 3 exams = K

No.of students cleared UPSC and BANK = 40

No.of students cleared UPSC and SSC = 49

No.of students cleared BANK and SSC = 35

X+K = 197-(40+49) = 108

Y+K = 207-(40+35) = 132

Z + K = 268 - ( 49+35) = 184

X+Y+Z+K = 500 - (40+49+35)= 376

From above equations

X=84 ; Y =108 ; Z = 160 ; K = 24

**Answers :**

**1.2**

K=24

**2.2**

Only UPSC = 84

Total no.of students = 500

% of only UPSC cleared = 84*100/500 = 16.8%

**3.5**

Who cleared at least two examination = 40+49+35+24=148

**4. 1**

who cleared BANK ,but not SSC = 148*100/500 = 29.6%

**5. 4**

= 84+108+160+160=352

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