1. The average of nine numbers are 87. If the average of first five numbers are 79 and the average of next three numbers are 92; find ninth number?

9 संख्याओं का औसत 87 है। यदि पहले 5 संख्याओं का औसत 79 है और अगले 3 संख्याओं का औसत 92 है; तो नौवीं संख्या ज्ञात कीजिए।


Option “A” is correct.

Given:

Average of nine numbers = 87

Average of first five numbers = 79

Average of next three numbers = 92

Formula used:

Sum of all observations = Average × Number of observations

Calculation:

Sum of all nine numbers = 87 × 9 = 783

Sum of first five numbers = 79 × 5 = 395

Sum of next three numbers = 92 × 3 = 276

Sum of first 8 numbers = 395 + 276 = 671

Ninth number = Sum of all nine numbers – Sum of first 8 numbers

⇒ Ninth number = 783 – 671 = 112

∴ Ninth number is 112

2. A scored 73, 76, 20 and 7 runs in four out of five innings. What should be his score in the fifth innings, if he has to make an average of 55 runs in five innings?

 A ने पांच पारियों में से चार पारियों में  73, 76, 20 और 7 बनाया। यदि उसे पांच पारियों में 55 रनों का औसत बनाना है, तो पांचवे पारी में उसका स्कोर क्या होना चाहिए।


Option “A” is correct.

Let the score in the fifth innings be x.

Average of five innings = 55

Sum of five innings = 55 × 5

According to the question

73 + 76 + 20 + 7 + x = 55 × 5

176 + x = 275

⇒ x = 275 – 176 = 99

3. Three number are in the ratio 1/2 : 2/3 : 3/4. The difference between the greatest and the smallest number is 27. The average of the three number is:

तीन संख्याएँ 1/2 : 2/3 : 3/4 के अनुपात में हैं। सबसे बड़ी और सबसे छोटी संख्या के बीच का अंतर 27 है। तीनों संख्याओं का औसत क्या है?


Option “A” is correct.

The given ratio of three numbers

1/2 : 2/3 : 3/4

⇒ 6 : 8 : 9

Let the numbers be 6x, 8x and 9x

According to question

Difference between the greatest and the smallest number = 27

⇒ 9x – 6x = 27

⇒ 3x = 27

⇒ x = 9

The first number = 6x = 6 × 9 = 54

The Second number = 8x = 8 × 9 = 72

The third number = 9x = 9 × 9 = 81

Sum of three numbers = 54 + 72 + 81 = 207

∴ Average = 207/3 = 69

4. A family consists of 5 elders and some children, such that the average age of the family is 28 years. If the average age of the elders and the children is 42 years and 18 years respectively, how many children are there in the family?

एक परिवार में 5 बड़े और कुछ बच्चे रहते हैं, इस प्रकार उनके परिवार की औसत आयु 28 वर्ष है। यदि बड़ों और बच्चों की औसत आयु क्रमशः 42 वर्ष और 18 वर्ष हो, तो परिवार में कितने बच्चे हैं?


Option “C” is correct.

Given:

Average of a family = 28 years

The average of 5 elders = 42 years

The average of children = 18 years

Formula used:

Average = Sum of observation/Total number of observation

Calculation:

Let there be ‘x’ children in the family.

⇒ Total age of x children = 18x years

⇒ Total age of 5 elders = 5 × 42 = 210 years

Now,

Total no. of family members = 5 + x

⇒ Total age of family = 28(5 + x) = 140 + 28x

⇒ 140 + 28x = 18x + 210

⇒ 10x = 70

⇒ x = 70/10 = 7

∴ There are 7 children in the family

5. Average of 12 numbers is 48. If each number is increased by 11, then what will be the new average?

12 संख्याओं का औसत 48 है। यदि प्रत्येक संख्या में 11 की वृद्धि होती है, तो नया औसत क्या होगा?


Option “A” is correct.

Given:

Average of 12 numbers = 48

Each number is increased by 11

Concept Used:

Average = Sum of observations/Total number of observations.

If each number is increased by x, then new average becomes “Old average + x”

Calculation:

The Average of 12 numbers = 48

Each number is increased by 11.

Then, the new average of 12 numbers = 48 + 11

∴ The new average will be 59.



6. Average of 49, 62, 37, 55 and x is 53. What is the value of x?

 49, 62, 37, 55 और x का औसत 53 है। x का मान क्या है?


Option “C” is correct.

Average = Sum of number/number of term

⇒ 53 = (49 + 62 + 37 + 55 + x)/5

⇒ 265 = 203 + x

⇒ x = 62

∴ The value of x is 62.

7.The average of 4 numbers is 9. If another number 14 is included, then what is the new average?

यदि 4 संख्याओं का औसत 9 है । और यदि एक अन्य संख्या 14 इनमें जोड़ दी जाए, तब नया औसत क्या होगा?


Option “B” is correct.

The average of 4 numbers = 9

⇒ Average = Sum of all numbers/Number of term

⇒ 9 = Sum of 4 numbers/4

⇒ Sum of 4 numbers = 36

⇒ Sum of 5 numbers = 36 + 14 = 50

⇒ New average = 50/5 = 10

∴ The new average is 10.

8. The daily average rainfall on 5 days of a week is 30 mm. If the rainfall on 6th and 7th day is 42 mm and 25 mm respectively, then what is the average daily rainfall for the 7 days?

सप्ताह के 5 दिनों की दैनिक औसत वर्षा 30 मिमी है। यदि 6 वें और 7 वें दिन की वर्षा क्रमशः 42 मिमी और 25 मिमी है, तो 7 दिनों के लिए औसत दैनिक वर्षा क्या है?


Option “A” is correct.

Calculation:

⇒ Sum of rainfall on 5 days = 5 × 30 = 150 mm

⇒ Sum of rainfall of whole week = 150 + 42 + 25 = 217 mm

⇒ Average rainfall for week = 217/7 = 31 mm


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9. 6 pencils cost Rs. 30 and 12 pens cost Rs. 120. What is the average cost of 50 pencils and 50 pens?

6 पेंसिल का मूल्य 30 रुपये और 12 पेन का मूल्य 120 रुपये है। 50 पेंसिल और 50 पेन का औसत मूल्य क्या है?


Option “D” is correct.

Cost of 6 pencils = Rs. 30

Cost of 1 pencil = 30/6 = Rs. 5

Cost of 50 pencils = 5 × 50 = 250

Cost of 12 pens = Rs. 120

Cost of 1 pens = 120/12 = Rs. 10

Cost of 50 pens = 10 × 50 = 500

Average cost of 50 pens and 50 pencils = (500 + 250)/100 = 750/100 = Rs. 7.5

10. In a class, the average score of thirty students in a test is 69. Later on, it was found that the score of one student was wrongly marked as 88 instead of 58. The actual average score is:

एक कक्षा में, एक परीक्षा में तीस छात्रों का औसत प्राप्तांक 69 है। बाद में, यह पाया गया कि एक छात्र के प्राप्तांक को गलत तरीके से 58 के बजाय 88 पढ़ा गया था। वास्तविक औसत प्राप्तांक है:


Option “B” is correct.

Average score of 30 students = 69

Sum of score of 30 students = 69 × 30 = 2070

Correct sum of score of 30 students = 2070 – 88 + 58 = 2040

∴ Correct average score of 30 students = 2040/30 = 68

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