UPSC NDA Math Model Paper 7

Ten numbers in increasing order are 10, 22, 26, 29, 34, x, 42, 67, 70, and y.
The mean is given by the formula:
⇒Mean =

∑xi

n

Given, Mean = 42
⇒42=

x+y+300

10

⇒ 420 = x + y + 300
⇒ 420 – 300 = x + y
⇒ x + y = 120
The median is given by the formula:
⇒Median=

T5+T6

2

Given, Median = 35
⇒35=

34+x

2

⇒ 70 = 34 + x
⇒ x = 70 – 34
∴ x = 36
On substituting ‘x’ in the equation from mean value,
⇒ 36 + y = 120
⇒ y = 84
Now,

y

x

=

84

36

∴

y

x

=

7

3