Quiz-1

Average = \frac{sum\, of observations}{No\, of\, observations}
Average = \frac{80+90+110+4th\, day}{4} = 80
Therefore 4rth day expenditure = Rs(320-280) =Rs 40

1 to 11 = 11 * 10.9 = 119.9

1 to 6 = 6 * 10.5 = 63

6 to 11 = 6 * 11.4 = 68.4

63 + 68.4 = 131.4 – 119.9 = 11.5

6th number = 11.5

Let age of three boys be =3x,5x and 7x
ATQ
The ratio of age of three boys= 3x + 5x + 7x =3* 15
3x + 5x + 7x =45
x =3

Hence, the age of youngest boy -> 3x = 3 x 3 = 9

Let the attendance on the three days be 2x, 5x and 13x respectively.
Then, total charges
= Rs. (15 × 2x + 7.50 × 5x + 2.50 × 13x)
= Rs. (30x + 37.5x + 32.5x)
= Rs. 100x
So, Average change per person
= Rs \frac{100x}{2x + 3x+ 5x}
= Rs 5

Let the four numbers be a, b, c and d.
a+b+c = 3x16 = 48 …(1)
b+c+d = 3x15 = 45 …(2)
a+d = 13 …(3)

Subtract (2) from (1); a-d = 48–45 = 3 …(4)

Add (3) and (4): 2a = 16 or a = 8, d = 5.

(1) becomes 8+b+c = 48, or b+c = 40 …(5)

a = 8, (b+c) = 40, d = 5.

1 to 9 = 9 * 9 = 81

1 to 5 = 5 * 10 = 50

5 to 9 = 5 * 8 = 40

5th = 50 + 40 = 90 – 81 = 9

According to the question,

The avg. of 10 numbers is = 15

Sum of 10 numbers are = 15×10=150

He mistakenly writes one number 26 instead of 36.

\therefore difference = 36 - 26 = 10

\therefore Actual sum of 10 numbers = 150 + 10 = 160

\therefore Actual average = \frac{160}{10} =16

Explanation : 16x + 85 = 17 ( x +3 )

16x + 85 = 17x + 51

X = 34. (Ans).

Let the average of 25 person be x
total age of a person=average×no.of person
total age of 25 person =25x
when a new person of 46kg come average decrease by 5kg(x-5)
Total age of 26 person =25x+46
Average age of 26 person=x-5
ATQ
25x+46=26(x-5)
25x+46=26x-130
26x-25x=130+46
x=176
hence the avg. of 25 person be 176kg.