Average
- Out of nine persons, 8 persons spent ₹30 each for their meals. The ninth one spent ₹20 more than the average expenditure of all the nine. The total money spent by all of them was
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Expenditure of 9th person = ₹ y
∴ y - y + 8 × 30 = 20 9 ∴ 9y - y - 240 = 20 9
⇒ 8y – 240 = 180
⇒ 8y = 240 + 180 = 420
Correct Option: C
Expenditure of 9th person = ₹ y
∴ y - y + 8 × 30 = 20 9 ∴ 9y - y - 240 = 20 9
⇒ 8y – 240 = 180
⇒ 8y = 240 + 180 = 420
⇒ y= 420÷8 = 525 .
Total expenditure = 52.5 + 240 = 292.5
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If the average of x and 1 / x (x ≠ 0) is M, then the average of x2 and 1 is : x²
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On the basis of given in question ,
x + 1 x = M 2 ⇒ x + 1 = 2M x Required average = x² + 1 x² 2 Required average = 
x + 1 
² - 2 x 2
Correct Option: C
On the basis of given in question ,
x + 1 x = M 2 ⇒ x + 1 = 2M x Required average = x² + 1 x² 2 Required average = x + 1 ² - 2 x 2 Required average = 4M² - 2 = 2M² - 1 2
- B was born when A was 4 years 7 months old and C was born when B was 3 years 4 months old. When C was 5 years 2 months old, then their average age was
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According to question ,
C = 5 years 2 months
B = 8 years 6 months
A = 13 years 1 month∴ Average = 26 years 9 months 3
Correct Option: D
According to question ,
C = 5 years 2 months
B = 8 years 6 months
A = 13 years 1 month∴ Average = 26 years 9 months 3 
321 = 26 years 9 months 
3 3
Average = 8 years 11 months
- The average mathematics marks of two Sections A and B of Class IX in the annual examination is 74. The average marks of Section A is 77.5 and that of Section B is 70. The ratio of the number of students of Section A and B is
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If the number of students in section A be p and that in section B be q, then
According to question,74 = 77.5 × p + q × 70 p + q
⇒ 74p + 74q = 77.5p + 70q
⇒ 77.5p – 74p = 74q – 70q
⇒ 3.5p = 4q
Correct Option: C
If the number of students in section A be p and that in section B be q, then
According to question,74 = 77.5 × p + q × 70 p + q
⇒ 74p + 74q = 77.5p + 70q
⇒ 77.5p – 74p = 74q – 70q
⇒ 3.5p = 4q⇒ p = 4 = 8 y 3.5 7
⇒ p : q = 8 : 7
Hence , The ratio of the number of students of Section A and B is 8 : 7 .
- The average of marks scored by the students of a class is 68. The average of marks of the girls in the class is 80 and that of boys is 60. What is the percentage of boys in the class ?
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Let the number of boys and girls in the class be p and q respectively.
∴ 60p + 80q = 68(p + q)
⇒ 60p + 80q = 68p + 68q
⇒ 8p = 12q
⇒ 2p = 3q ⇒ q = 2 / 3p∴ Required percentage = p × 100 p + q Required percentage = x × 100 p + 2 p 3 Required percentage = 3p × 100 3p + 2q Required percentage = 3 × 100 = 60% 5
Second method to find the required percentage : By Alligation method
According to the question,
Correct Option: B
Let the number of boys and girls in the class be p and q respectively.
∴ 60p + 80q = 68(p + q)
⇒ 60p + 80q = 68p + 68q
⇒ 8p = 12q
⇒ 2p = 3q ⇒ q = 2 / 3p∴ Required percentage = p × 100 p + q Required percentage = x × 100 p + 2 p 3 Required percentage = 3p × 100 3p + 2q Required percentage = 3 × 100 = 60% 5
Second method to find the required percentage : By Alligation method
According to the question,
Ratio of girls to boys = 8 : 12 = 2 : 3∴ Percentage of boys = 3 × 100 = 60% 5
