model 4 find nth average from 1st & last number Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [SSC CHSL DEO & LDC 2010]

The average temperature of the first 4 days of a week was 37°C and that of the last 4 days of the week was 41°C. If the average temperature of the whole week was 39°C, the temperature of the fourth day was

a) 38.5°C

b) 40°C

c) 39°C

d) 38°C

Answer: (c)

Using Rule 1,

M + T + W + TH = 4 × 37 = 148°C ........ (i)

TH + F + S + S = 4 × 41 = 164°C ........ (ii)

M + T +....+ S + S = 7 × 39 = 273°C ........ (iii)

∴ The temperature of the fourth day

= 148 + 164 – 273 = 39°C

Question : 2

The average of 15 numbers is 7. If the average of the first 8 numbers is 6.5 and the average of the last 8 numbers is 8.5, then the middle number is :

a) 23

b) 15

c) 13

d) 10

Answer: (b)

Middle i.e. eighth number

= 8 × 6.5 + 8 × 8.5 – 15 × 7

= 52 + 68 – 105

= 120 – 105 = 15

Question : 3 [SSC CGL 2008]

In a certain year, the average monthly income of a person was Rs.3,400. For the first eight months of the year, his average monthly income was Rs.3,160 and for the last five months, it was Rs.4,120. His income in the eighth month of the year was

a) Rs.5,080

b) Rs.5,520

c) Rs.15,520

d) Rs.3,160

Answer: (a)

Using Rule 1,

Person’s income in the eighth month

= Rs.(3160 × 8 + 5 × 4120 – 12 × 3400)

= Rs. (25280 + 20600 – 40800)

= Rs. 5080

Question : 4 [SSC CGL Tier-I 2016]

The average of two numbers is 8 and the average of other three numbers is 3. The average of the five numbers is :

a) 3

b) 6

c) 5

d) 2

Answer: (c)

Average of five numbers

= ${2×8+3×3}/{2+3}$

= ${16+ 9}/5$ = $25/5$ = 5

Question : 5 [SSC CGL Tier-II 2013]

The average of 11 results is 50. If the average of the first six results is 49 and that of the last six is 52, the sixth no. is

a) 50

b) 56

c) 52

d) 48

Answer: (b)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sum of observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Sixth result

= 6 × 49 + 6 × 52 – 11 × 50

= 294 + 312 – 550 = 56

IMPORTANT quantitative aptitude EXERCISES

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