The average height of a certain number of students in a group is 155.6 cm. If 12 students having an average height of 150.5 cm join the group and 7 students having an average height of 159 cm leave the group, the average height of the students in the group will decrease by 34 mm. What is the number of students, initially, in the group?
Answers
Answer:
20
it's ssc question
Let the total number of students is x.
34mm=3.4cm
Next, total height of the students is =155.6x
(155.6x+12*150.5-7*159)/x+12-7=155.6-3.4
155.6x+1806-1113/x+5=152.2
155.6x+693=152.2x+761
3.4x=68
x=68/3.4
x=680/34
x=20ans
Best of Luck
Step-by-step explanation:
Let there were x students initially.
The average height of a certain number of students in a group is 155.6 cm.
Then the sum of the heights
= x * 155.6 cm
= 155.6x cm
12 students having an average height of 150.5 cm join the group and 7 students having an average height of 159 cm leave the group.
Then the new sum of heights
= 155.6x + 150.5 × 12 - 159 × 7 cm
= 155.6x + 693 cm
Total number of students in the group
= x + 12 - 7 = x + 5
Average height of x + 5 students
= (155.6x + 693)/(x + 5) cm
Here, 34 mm = 3.4 cm
The average height of the students in the group will decrease by 34 mm.
Then (155.6x + 693)/(x + 5) = 155.6 - 3.4
⇒ 155.6x + 693 = 152.2x + 761
⇒ 155.6x - 152.2x = 761 - 693
⇒ 3.4x = 68
⇒ 34/10 * x = 68
⇒ x = 68 * 10/34
⇒ x = 20
Final answer: 20 students
Initially there were 20 students in the group.
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