Average questions with tricks for ssc cgl and ssc 10 plus 2 exam

1

Consider the sequence of 5 consecutive integers. If the average of first three is t. The average of all five integers is:

» Explain it

Correct Option: B

Let the 3 integers be

a – 1, a, a + 1. then average is-

⇒	a – 1 + a + a + 1	=	3a	= t ⇒ a = t.
	3		3

Similarly, the average of 5 numbers is

⇒	a–1 + a + a+1 + a+2 + a+3	=	5a + 5	= (a + 1) = t + 1.
	5		5

Hence, option B is correct.

1

लगातार 5 पूर्णांकों के अनुक्रम पर विचार करें। यदि प्रथम तीन का औसत t है । सभी पांच पूर्णांकों का औसत होगा:

» Explain it

सही विकल्प : B

Let the 3 integers be

a – 1, a, a + 1. then average is-

⇒	a – 1 + a + a + 1	=	3a	= t ⇒ a = t.
	3		3

Similarly, the average of 5 numbers is

⇒	a–1 + a + a+1 + a+2 + a+3	=	5a + 5	= (a + 1) = t + 1.
	5		5

Hence, option B is correct.

2

The arithmetic mean of the following numbers

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6 and 7, 7, 7, 7, 7, 7, 7, is

» Explain it

Correct Option: B

Required mean =	1 × 1 + 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5 + 6 × 6 + 7 × 7
	1 + 2 + 3 + 4 + 5 + 6 + 7

⇒	1²+ 2² + 3²+ ...... + 7²
	1 + 2 + 3 + ........+ 7

⇒

n(n + 1)(2n + 1)

6

[∵ sum of squares of n natural numbers]

n(n + 1)

2

[∵ sum of n natural numbers]

⇒	(2n + 1)	⇒	2 × 7 + 1	=	15	= 5.
	3		3		3

Hence, option B is correct.

2

निम्नलिखित संख्याओं का समांतर माध्य क्या होगा?

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6 और 7, 7, 7, 7, 7, 7, 7

» Explain it

सही विकल्प : B

Required mean =	1 × 1 + 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5 + 6 × 6 + 7 × 7
	1 + 2 + 3 + 4 + 5 + 6 + 7

⇒	1²+ 2² + 3²+ ...... + 7²
	1 + 2 + 3 + ........+ 7

⇒

n(n + 1)(2n + 1)

6

[∵ sum of squares of n natural numbers]

n(n + 1)

2

[∵ sum of n natural numbers]

⇒	(2n + 1)	⇒	2 × 7 + 1	=	15	= 5.
	3		3		3

Hence, option B is correct.

3

If average weight of a family is ‘y’ kg. If a guest weighing 30 kg arrives then the average weight is increases by 1 kg. If the weight of this guest had been 18 kg then the average weight of the family would have decreased by 1 kg. Find ‘y’.

» Explain it

Correct Option: B

Let the number of family members be x.

Therefore, the total weight = xy

Equation in the 1st scenario:

(x + 1) (y + 1) = xy + 30

xy + x + y + 1 = xy + 30

x + y = 29 .....(i)

Equation in the 2nd scenario:

(x + 1) (y - 1) = xy + 18

xy + y - x - 1 = xy + 18

y - x = 19 ....(ii)

Solving equtions (i) and (ii), we get

2y = 48, Therefore, y = 24.

Hence, option B is correct.

3

यदि एक परिवार का औसत भार 'y' kg है। अगर कोई मेहमान 30 किलो वजन का आता है तो औसत वजन 1 किलो बढ़ जाता है। अगर इस मेहमान का वजन 18 किलो होता तो परिवार के औसत वजन में 1 किलो की कमी होती। 'y' खोजें।

» Explain it

सही विकल्प : B

Let the number of family members be x.

Therefore, the total weight = xy

Equation in the 1st scenario:

(x + 1) (y + 1) = xy + 30

xy + x + y + 1 = xy + 30

x + y = 29 .....(i)

Equation in the 2nd scenario:

(x + 1) (y - 1) = xy + 18

xy + y - x - 1 = xy + 18

y - x = 19 ....(ii)

Solving equtions (i) and (ii), we get

2y = 48, Therefore, y = 24.

Hence, option B is correct.

4

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?

» Explain it

Correct Option: D

Sixth results = total no. of first six reuslth + total no. of last six results – total no. of 11 results

= (6 × 49) + (6 × 52) – (11 × 50)

= 294 + 312 – 550 = 56.

Hence, option D is correct.

4

11 परिणामों का औसत 50 है। यदि पहले छह परिणामों का औसत 49 है और अंतिम छह परिणामों का औसत 52 है। तो छठी संख्या क्या होगी?

» Explain it

सही विकल्प : D

Sixth results = total no. of first six reuslth + total no. of last six results – total no. of 11 results

= (6 × 49) + (6 × 52) – (11 × 50)

= 294 + 312 – 550 = 56.

Hence, option D is correct.

5

A number is such that when it is multiplied by 8, it gives another number which is as much above from 270 as the original number (itself) is below 270. The average of the original number and the resultant number is:

» Explain it

Correct Option: D

Let the number be x then.

270 – x = 8x – 270

⇒ x = 60 and 8x = 480

Therefore the average of 60 and 480 is 270.

Hence, option D is correct.

5

एक संख्या ऐसी है कि जब इसे 8 से गुणा किया जाता है, तो यह एक और संख्या देती है जो 270 से उतनी ही अधिक होती है जितनी कि मूल संख्या 270 से कम होती है। मूल संख्या और परिणामी संख्या का औसत क्या होगा?

» Explain it

सही विकल्प : D

Let the number be x then.

270 – x = 8x – 270

⇒ x = 60 and 8x = 480

Therefore the average of 60 and 480 is 270.

Hence, option D is correct.