41. In a group of 10 men, 2 men aged 20 years and 24 years were replaced by two new men. Due to this, the average age of the group increased by 3 years. What is the average age of the 2 new men?

10 पुरुषों के एक समूह में, 20 वर्ष और 24 वर्ष की आयु के 2 पुरुषों को दो नए पुरुषों से बदल दिया गया। इसके कारण, समूह की औसत आयु में 3 वर्ष की वृद्धि हुई। 2 नए पुरुषों की औसत आयु क्या है?

Option “B” is correct.

According to question

Average of 10 men increased by 3,

⇒ The total age of men increased by 10 × 3 = 30 years

⇒ Sum of ages of two new men = 20 + 24 + 30 = 74 years

∴ Average age of 2 new men = 74/2 = 37 years 

42. Average of 40 numbers is 71. If the number 100 replaced by 140, then average is increased by.

40संख्याओं का औसत 71 है। यदि संख्या 100 को 140 से बदल दिया जाता है, तो औसत में वृद्धि हुई है।

Option “D” is correct.

Given:

Average of 40 numbers = 71

Formula:

Average = Sum of all observations/Total number of all observations

Calculation:

Sum of 40 numbers = 40 × 71 = 2840

New sum of 40 numbers = 2840 – 100 + 140 = 2880

New average of 40 numbers = 2880/40 = 72

∴ The average increased = 72 – 71 = 1

Shortcut Trick 

New average = Old average + (Change in number/Total numbers)

New average of 40 numbers = 71 + (140 – 100)/40 = 71 + 1 = 72

∴ The average increased = 72 – 71 = 1 

43. If out of 8 employees of the company, 2 were of 30 years, 3 of 25 years and 3 of 35 years, find their average age:

यदि एक कंपनी के 8 कर्मचारियों में से, 2 की आयु 30 वर्ष, 3 की 25 वर्ष और 3 की 35 वर्ष है, तो उनकी औसत आयु ज्ञात कीजिये:

Option “B” is correct.

Given:

Total employees = 8

Age of the first lot = 30 years

Age of the second lot = 25 years

Age of the third lot = 35 years

Concept:

Average = Total sum/ Total persons

Calculation:

Sum of their ages = (2 × 30) + (3 × 25) + (3 × 35)

= 60 + 75 + 105

= 240

Average age = Total age / Number of persons

= 240/8

= 30 years

44. There are 20 species of fishes listed in a pond with an average of 47 fishes per species. It is found that a species listed 62 fishes is wrongly written as 22. Find the correct average. 

एक तालाब में मछलियों की 20 प्रजातियाँ सूचीबद्ध हैं प्रति प्रजाति 47 मछलियों की औसत के साथ। यह पाया गया है कि 62 मछलियों को सूचीबद्ध करने वाली एक प्रजाति को गलत तरीके से 22 लिखा गया है। सही औसत ज्ञात कीजिए।

Option “C” is correct.

Given:

Total number of species = 20

Average of fishes per species = 47

Concept used:

New average = Given average + (Difference of actual and wrongly written)/Total number of species

Calculation:

The difference between actual and wrongly written numbers = 62 – 22 = 40

Hence,

Required average = 47 + 40/20

⇒ Required average = 47 + 2 = 49

∴ The correct average of fishes is 49.

45. The average mark of 50 students is 75. If the marks obtained by one of the student had been written as 36 instead of 86, then the corrected average of marks is:

50 छात्रों के अंकों का औसत 75 है। यदि किसी छात्र द्वारा प्राप्त अंकों को 86 के बजाय 36 लिख दिया गया है, तब अंकों का सही औसत क्या है?

Option “B” is correct.

Given:

The average marks of 50 students = 75

Marks of one student is written as 36 instead of 86.

Formula Used:

Sum of all numbers = Average of numbers × Number of terms

Calculation:

The total marks obtained by 50 students = 75 × 50

= 3750

Marks of one student is written as 36 instead of 86.

Actual marks = 3750 + (86 – 36)

= 3750 + 50

= 3800

Correct average = Actual marks/total number of students

= 3800/50

= 76

∴ The correct average marks of 50 students is 76.

Shortcut Trick

Correct average = Old average + (Error/Number of students)

= 75 + (86 – 36)/50

= 75 + 50/50

= 75 + 1

= 76

∴ The correct average marks of 50 students is 76.

46.Find the average.
14, 22, 38, 58, 78 & 24

औसत ज्ञात कीजिए।

Option “A” is correct.

Given:

Numbers are 14, 22, 38, 58, 78 and 24

Formula used:

Average = Sum of Observations/Number of observations

Calculation:

Sum of observations = 14 + 22 + 38 + 58 + 78 + 24 = 234

Number of observations = 6

Average = 234/6 = 39

∴ The required average is 39

47.If the population of a town increases by 25% in the first year and increases by 36% in the second year, then what is the average rate (in percentage)of increase in the population?

यदि एक शहर की जनसँख्या में पहले वर्ष में 25% की वृद्धि होती है और दूसरे वर्ष में दूसरे 36% की वृद्धि होती है, तब जनसँख्या में वृद्धि की औसत दर (प्रतिशत में) क्या है?

Option “D” is correct.

GIVEN:

Increase in population

First year = 25%, Second year = 36%

FORMULA USED:

Average rate of increase (in %) = (1/2) × Total increment × 100

CALCULATION:

Let the initial population of town be 100.

Population after first year = 100 + 25% of 100 = 100 + 25 = 125

Population after second year = 125 + 36% of 125 = 125 + 45 = 170

Total increment = (170 – 100)/100 = 7/10

∴ Average rate of increase (in %) = (1/2) × (7/10) × 100 = 35%

Alternate Method Equivalent increase = 25 + 36 + (25 × 36)/100 = 70%

Average increase = 70/2 = 35%.

∴ The average increase is 35%.

48. The average temperature from Monday to Wednesday is 17°C and the average temperature from Tuesday to Thursday is 15°C. The temperature on Thursday is 4/5th of the temperature on Monday. Find the temperature on Thursday

सोमवार से बुधवार तक औसत तापमान 17° सेल्सियस है और मंगलवार से बृहस्पतिवार तक औसत तापमान 15° सेल्सियस है। बृहस्पतिवार को तापमान, सोमवार के तापमान का 4/5 है। बृहस्पतिवार को तापमान ज्ञात कीजिये।

Option “C” is correct.

Monday + Tuesday + Wednesday = 17 × 3 = 51°C and

Tuesday + Wednesday + Thursday = 15 × 3 = 45°C

Subtracting both equations :

⇒ Monday  – Thursday = 6°C

Given that the temperature on Thursday is 4/5th of the temperature on Monday;

∴ Thursday : Monday = 4 : 5

∴ Temperature on Thursday = 6 × 4 = 24°C

49. The mean of 20 numbers is 60. If two numbers 35 and 85 are removed, then what will be the mean of remaining numbers?

20 संख्याओं का औसत 60 है। यदि दो संख्याएँ 35 और 85 हटा दी जाती हैं, तो शेष संख्याओं का माध्य क्या होगा?

Option “C” is correct.

Average of 20 numbers is 60

∴ Sum of these 20 numbers = 20 × 60 = 1200

If two numbers 35 and 85 are removed

Sum of remaining 18 numbers = 1200 – 35 – 85 = 1080

∴ Average of these 18 numbers = 1080/18 = 60

50. In an examination, the average mark scored by 60 students is 55. On complaint by three students, it was found that their marks were wrongly entered as 6, 6 and 3 instead of 96, 60 and 39 respectively. What is the correct average mark scored by the students in the examination?

एक परीक्षा में, 60 छात्रों द्वारा प्राप्त औसत अंक 55 हैं। तीन छात्रों की शिकायत पर, यह पाया गया कि उनके अंकों को क्रमशः 96, 60 और 39 के बजाय 6, 6 और 3 लिखा गया था। परीक्षा में छात्रों द्वारा बनाए गए सही औसत अंक क्या हैं?

Option “C” is correct.

GIven:

The average marks scored by 60 students is 55.

It was found that their marks were wrongly entered as 6, 6 and 3 instead of 96, 60 and 39 respectively.

Concept used:

Total weight = Average weight × Number of boxes

Calculation:

Average marks before correction = 55

Total marks scored before correction = 60 × 55

⇒ 3300

∵ The marks 6, 6, 3 were wrongly entered instead of 96, 60 and 39,

Total marks scored after correction = 3300 – 6 – 6 – 3 + 96 + 60 + 39

⇒ 3480

No. of students = 60

Correct average marks scored in examination = 3480/60

⇒ 58

∴ The correct average mark scored by the students in the examination is 58.

Pages: 1 2 3 4 5 6 7 8

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