Question : Directions: In a college, the total number of students who opted for Biology or Chemistry is 150. Later, 12 students who opted for Biology changed their preference and opted for Chemistry. Now, the number of students in Biology is half the number of students in Chemistry. How many students are in Chemistry now?
Option 1: 88
Option 2: 94
Option 3: 104
Option 4: 100
Correct Answer: 100
Solution : Given: The total number of students = 150 Let the number of students who opted for biology = x and the number of students who opted for chemistry = y This means – x + y = 150 — (i) Now, 12 students who opted for Biology changed their preference and opted for Chemistry. So, the new number of students who opted for biology = x – 12 and the new number of students who opted for chemistry = y + 12
The number of students in Biology is half the number of students in Chemistry – (x – 12) = (y + 12) ÷ 2 2(x – 12) = y + 12 2x – 24 = y + 12 2x – y = 36 — (ii) Adding the equations (i) and (ii) – x + y + 2x – y = 150 + 36 3x = 186 x = 186 ÷ 3 x = 62 Now, put the value of x in the equation (i) – 62 + y = 150 y = 150 – 62 = 88
So, the students who opted for chemistry now are (88 + 12) = 100. Hence, the fourth option is correct.
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Question : Directions: Which of the following numbers will replace the question mark (?) in the given series? 102, 100, ?, 96, 112
Option 1: 98
Option 2: 100
Option 4: 108
Question : Directions: Select the number that will replace the question mark (?) in the following series. 65, 88, 77, 98, 91, 108, ?, 118, 125
Option 1: 104
Option 2: 95
Option 3: 99
Option 4: 107
Question : Directions: In a class of 120 students, 100 students participate in either Golf or Skating, or both. Among them, a total of 60 students participate in Golf. A total of 56 students participate in Skating. How many students participate only in Skating?
Option 1: 40
Option 2: 16
Option 3: 44
Option 4: 36
Question : Select the option that expresses the given sentence in indirect speech. She said to me, "I was thinking of going out for dinner but had changed my mind later on."
Option 1: She said me that she was thinking of going out for dinner but changed her mind later on.
Option 2: She said that she thought of going out for dinner but changed her mind later on.
Option 3: She told me that I was thinking of going out for dinner but changed my mind later on.
Option 4: She told me that she had been thinking of going out for dinner but changed her mind later on.
Question : Directions: In an examination, Rahul got the 11th rank and he was 47th from the bottom among those who passed, 3 students could not appear for the exam. 1 student failed. What is the total number of students in the class?
Option 1: 60
Option 2: 62
Option 3: 59
Option 4: 61
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