RD Sharma Class 9 Solutions Chapter 24 VSAQS: RD Sharma Class 9 Solutions Maths Chapter 24 VSAQS PDF files are available free of charge. This PDF has been created by our team of experts. These solutions are very useful for class 9 exams. As detailed, students can view these solutions while preparing for exams.
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Question 1: If the ratio of mean and median of a certain data is 2:3, then find the ratio of its mode and mean.
Solution:
Empirical formula: Mode = 3 median – 2 mean
Since, ratio of mean and median of a certain data is 2:3, then mean = 2x and median = 3x
Mode = 3(3x) – 2(2x)
= 9x – 4x
= 5x
Therefore,
Mode: Mean = 5x:2x or 5: 2
Question 2: If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
Solution: We know, Empirical formula: Mode = 3 Median – 2 Mean
Since, ratio of mode and median of a certain data is 6:5.
⇒ Mode/Median = 6/5
or Mode = (6 Median)/5
Now,
(6 Median)/5 = 3 Median – 2 Mean
(6 Median)/5 – 3 Median = – 2 Mean
or 9/10 (Median) = Mean
or Mean/ Median = 9/10 or 9:10.
Question 3: If the mean of x+2, 2x+3, 3x+4, 4x+5 is x+2, find x.
Solution:
Given: Mean of x+2, 2x+3, 3x+4, 4x+5 is x+2
We know, Mean = (Sum of all the observations) / (Total number of observations)
Sum of all the observations = x+2 + 2x+3 + 3x+4 + 4x+5 = 10x + 14
Total number of observations = 4
⇒ Mean = (10x + 14)/4
or (x + 2) = (10x + 14)/4 (using given)
4x + 8 = 10x + 14
x = -1
Question 4: The arithmetic mean and mode of a data are 24 and 12 respectively, then find the median of the data.
Solution:
Given: The arithmetic mean and mode of a data are 24 and 12 respectively
We know, Empirical formula: Mode = 3 Median – 2 Mean
or 3 Median = Mode + 2 Mean
Using given values, we get
3 Median = 12 + 2(24) = 60
or Median = 20
Question 5: If the difference of mode and median of a data is 24, then find the difference of median and mean.
Solution:
Given: difference of mode and median of a data is 24.
That is, Mode – Median = 24
or Mode = 24 + Median …(1)
We know, Empirical formula: Mode = 3 Median – 2 Mean
24 + Median = 3 Median – 2 Mean
(Using (1))
24 = 2 Median – 2 Mean
or 12 = Median – Mean
Therefore, the difference of median and mean is 12.
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