model 6 find average of excluded number Practice Questions Answers Test with Solutions & More Shortcuts

Question : 16 [SSC SO 2005]

There were 35 students in a hostel. If the number of students is increased by 7 the expenditure on food increases by Rs.42 per day while the average expenditure of students is reduced by Rs.1. What was the initial expenditure on food per day ?

a) Rs.432

b) Rs.442

c) Rs.400

d) Rs.420

Answer: (d)

Suppose the initial expenditure per day = Rs. x

⇒ $x/35$ - ${x+42}/42$ = 1

⇒ ${6x-5x-210}/210 = 1$

⇒ x = 210 + 210 = Rs. 420

Question : 17

The average of 6 observations is 45.5. If one new observation is added to the previous observations, then the new average becomes 47. The new observation is

a) 56

b) 50

c) 58

d) 46

Answer: (a)

Let the new observation be x. Then,

${x+6×45.5}/7$= 47

⇒ x + 273 = 47 × 7 = 329

⇒ x = 329 – 273 = 56

Aliter : Using Rule 24,

Here, x = (47 – 45.5) = 1.5, n = 6

New observation = Average + x (n + 1)

= 45.5 + 1.5 (6 + 1)

= 45.5 + 10.5 = 56

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