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The average age of students in a class was 15 years. When 5 new boys whose average age was 12 years 6 months were admitted in the class, the average age was reduced by 6 months. How many students were there in the class originally?

1. 15
2. 20
3. 18
4. 16

एक कक्षा में छात्रों की औसत आयु 15 वर्ष थी। जब 5 नए लड़के जिनकी औसत आयु 12 वर्ष 6 माह थी, को कक्षा में प्रवेश दिया गया तो औसत आयु 6 माह कम हो गई। मूल रूप से कक्षा में कितने छात्र थे?

1. 15
2. 20
3. 18
4. 16

This Question came in

UGC-NET-Hindi-30-September-2022-Shift-1-Q25

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Detailed Explanation & Answer

Let the number of students in the class originally = x

Average = ( sum of age of x students)/ number of students

So, sum of age of x students = 15*x.

Similarly, sum of age of 5 students = 5*(12.5)= 62.5.

Now, after addition of 5 students, new average becomes 14.5,

Average= sum of age of all students/ total number of students (i.e. x+5)

14.5= (15x + 62.5) / ( x+5)
14.5(x+5) = (15x + 62.5)
14.5x + 72.5 = 15x + 62.5
15x-14.5x = 72.5-62.5
0.5x = 10
x = 20

माना कि कक्षा में मूलतः विद्यार्थियों की संख्या = x है

औसत = (x छात्रों की आयु का योग)/ छात्रों की संख्या

तो, x छात्रों की आयु का योग = 15*x.

इसी प्रकार, 5 विद्यार्थियों की आयु का योग = 5*(12.5)= 62.5.

अब, 5 छात्रों को जोड़ने के बाद, नया औसत 14.5 हो जाता है,

औसत=सभी छात्रों की आयु का योग/छात्रों की कुल संख्या (अर्थात x+5)

14.5= (15x + 62.5) / ( x+5)
14.5(x+5) = (15x + 62.5)
14.5x + 72.5 = 15x + 62.5
15x-14.5x = 72.5-62.5
0.5x = 10
X= 20

The Correct Answer is 2

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