EXERCISE 6.A (OBJECTIVE TYPE QUESTIONS) (IN 26 30 SOLUTION)

26.       A car owner buys petrol at Rs. 7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if be spends Rs. 4000 each year?

a)      Rs. 7.98

b)      Rs. 8

c)       Rs.8.50

d)      Rs. 9

27.       The average of six numbers is X and the average of three of these is Y. If the average of the remaining three is z, then:

a)      X = y + z

b)      2 X = Y + z

c)       X = 2y + 2z

d)      None of these

28.       Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money sent by all of them was:

a)      Rs. 26

b)      Rs.290

c)       Rs. 295.50

d)      Rs.400.50

29.       The average of 50 numbers is 30. Each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was:

a)      28.32

b)      28.78

c)       29.27

d)      29.68

30.       The average of five numbers is 27. If two numbers is excluded, the average becomes 25, the excluded number is:

a)      25

b)      27

c)       30

d)      35

ANSWERS 

26.A

27.B

28.C

29.D

30.D

SOLUTION 

26.       Total quantity of petrol consumed in 3 years = (4000 / 7.50 + 4000 / 8 + 4000 / 8.50 ) litres

= 4000 ( 2 / 15 + 1/8 + 2/17 ) = (767000 / 51 ) litres.

Total amount spent = Rs. (3 x 4000) = Rs. 12000.

Average cost = Rs. (12000 x 51 / 767000) = Rs. 6120 / 767 = Rs.7.98.

27.       Clearly, we have : X = (3y + 3z / 6) or 2X = Y + z.

28.       Let the average expenditure be Rs. X. then,

9x = 8 x 30 + (x + 20) or 9X = X + 260 or 8X = 260 or X = 32.50.

Total money spent = 9X = Rs.(9 x 32.50) = Rs 292. 50.

29.       Sum of 50numbers = 30 x 50 = 1500.

Sum of remaining 48 numbers = 1500 – (35 + 40) = 1425.

Required average = (1425 / 48) = 475 / 16 = 29.68.

30.       Excluded number = (27 x 5) – (25 x 4) = 135 – 100 = 35.