**1) The average age of P and Q is 25 years. If P is to be replaced by R, the average would be 22 years. The average age of R and P is 21 years. Then find the ages of P, Q and R?**

**Option 1:**24 years, 26 years, 18 years

**Option 2:**28 years, 26 years, 18 years

**Option 3:**24 years, 30 years, 18 years

**Option 4:**24 years, 26 years, 36 years

**Option 5:**24 years, 32 years, 18 years

**Answer:**

**1:**24 years, 26 years, 18 years

**Explanation:**

**P + Q = 25 × 2 = 50 years ….. (i)**

**Q + R = 22 × 2 = 44 years ……( ii)**

**R + P = 21 × 2 = 42 years ….. (iii)**

**(i) + (ii) + (iii)**

**2(P + Q + R) = 136**

**P + Q + R = 68 . . . (iV)**

**By solving (i) and (iv)**

**R = 18 years**

**By solving (ii) and (iv)**

**P = 24 years**

**By solving (iii) and (iv)**

**Q = 26 years**

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**2) The average age of P and Q is 25 years. If P is to be replaced by R the average would be 22 years. The average age of R and P is 21 years. Then find the ages of P, Q and R?**

**Option 1:**24 years, 26 years, 18 years

**Option 2:**28 years, 26 years, 18 years

**Option 3:**24 years, 30 years, 18 years

**Option 4:**24 years, 26 years, 36 years

**Option 5:**24 years, 32 years, 18 years

**Answer:**

**1:**24 years, 26 years, 18 years

**Explanation:**

Solution:

**P + Q = 25 × 2 = 50 years ….. (i)**

**Q + R = 22 × 2 = 44 years ……( ii)**

**R + P = 21 × 2 = 42 years ….. (iii)**

**(i) + (ii) + (iii)**

**2(P + Q + R) = 136**

**P + Q + R = 68 . . . (iV)**

**By solving (i) and (iv)**

**R = 18 years**

**By solving (ii) and (iv)**

**P = 24 years**

**By solving (iii) and (iv)**

**Q = 26 years**

**General English Quiz - 10th August**

Reasoning Quiz- 10th August

Reasoning Quiz- 10th August

**3) The average age of 16 students and their teacher's age is 16 years. If the teacher's age is excluded, the average reduces by 2. What is the teacher's age?**

**Option 1:**36

**Option 2:**30

**Option 3:**38

**Option 4:**48

**Option 5:**32

**Answer:**

**4:**48

**Explanation:**

Solution:

**16S + T = 16 × 17**

**16S + T = 272 years**

**After excluding the age of teacher average of 16 students are,**

**16S = 14 × 16**

**= > 224 years**

**Therefore teacher’s age = 272 – 224 = 48 years**

**4) Directions : The following questions are accompanied by three statements (I), (II) and (III). You have to determine which statements(s) is /are sufficient /necessary to answer the following question.**

What will be the difference of two numbers?

I : The smaller number is 6 less than the average of two numbers.

II : The ratio between half of the bigger number to one third of the average of the numbers is 18 : 11.

दोनो संख्याओं का अंतर क्या होगा?

I: छोटी संख्या दोनों संख्याओं के औसत से 6 कम है।

II: बड़ी संख्या के आधे और संख्याओ के औसत के एक तिहाई के बीच 18: 11 का अनुपात है।

**Option 1:**Only I is sufficient

**Option 2:**Only II is sufficient

**Option 3:**Either I or II is sufficient

**Option 4:**Both I and II together are sufficient

**Option 5:**Neither I nor II is sufficient

**Answer:**

**4:**Both I and II together are sufficient

**Explanation:**

Solution:

Let the bigger number be x and smaller be y

Statement I:

y =

*x+y/2- 6*

2y = x + y – 12

x – y = 12

Statement II:

(x/2) / {(x+y)/3*2} = 18/11

5x – 6y = 0

Statement I and statement II

x = 72

**y = 60**

**Required difference = 72 – 60 = 12**

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**5) Therefore, both the statements are required to answer**

**Directions : The following questions are accompanied by three statements (I), (II) and (III). You have to determine which statements(s) is /are sufficient /necessary to answer the following question.**

The average of the first four numbers is two times of the fifth number. What is the fifth number?

I : The average of the first two numbers is 9 less than the average of the next two numbers.

II : The average of the first two numbers is 2.5 more than the fifth number.

III : The average of all five numbers is 12.6.

पहले चार संख्याओं का औसत पांचवें संख्या का दो गुना है। पांचवी संख्या क्या है?

I: पहली दो संख्याओं का औसत अगले दो संख्याओं के औसत से 9 कम है।

II: पहले दो संख्याओं का औसत पांचवें संख्या से 2.5 अधिक है।

III: सभी पांच संख्याओं का औसत 12.6 है।

**Option 1:**Only I 2

**Option 2:**Only II

**Option 3:**Only III

**Option 4:**Either I or II and III

**Option 5:**Any two of three Statements are sufficient to answer

**Answer:**

**3:**Only III

**Explanation:**

**Solution:**

Let the number be P, Q, R, S, and T where P is the first number, Q is the second number and so on.

According to question,

(P + Q + R + S)/4 = 2T

From I,

(P + Q)/2 = (R + S)/2 – 9

From II,

(P + Q)/2 = T + 2.5

From III,

P + Q + R + S + T = 5 × 12.6

⇒P + Q + R + S + T = 63----(i)

Given,

(P + Q + R + S)/4 = 2T

⇒P + Q + R + S = 8T----(ii)

From (i) and (ii), we get

8T + T = 63

⇒9T = 63

⇒T = 7

∴ Fifth number = 7

**6) Directions : The following questions are accompanied by three statements (I), (II) and (III). You have to determine which statements(s) is /are sufficient /necessary to answer the following question.**

The age of three friends A, B and C is (x + 6) years, (x - 4) years and (x+2) years resp. Find the age of A.

I: The average age of A and B taken together is (x - 27) years less than the average age of A and C taken together.

II: The average age of A and B taken together is 2 years more than the average age B and C taken together.

**Option 1:**Only I is sufficient

**Option 2:**Only II is sufficient

**Option 3:**Either I or II is sufficient

**Option 4:**Both I and II together are sufficient

**Option 5:**Neither I nor II is sufficient

**Answer:**

**1:**Only I is sufficient

**Explanation:**

**From statement I:**

**{(x+6) + (x-4)}/2 = {(x+6)+(x+2)}/2 – (x-27)**

**(2x+2)/2 = (2x+8-2x+54)/2**

**2x = 60**

**X = 30 years**

**A’s age = 30 + 6 = 36 years**

**Statement I is sufficient ot answer.**

**From statement II:**

**{(x+6)+(x-4)}/2 = 2 + {(x-4)+(x+2)}/2**

**(2x+2)/2 = (4+2x-2)/2**

**2x + 2 = 2x + 2**

**Statement II is not sufficient to answer.**

**7) Directions : The following questions are accompanied by three statements (I), (II) and (III). You have to determine which statements(s) is /are sufficient /necessary to answer the following question.**

Average age of employees working in Bank is 40 years. Next year, 30 employees will retire. What will be the average age of remaining employees next year?

**Statement I:**There are 80 employees in bank

**Statement II:**Retirement age is 55 year.

**Option 1:**Only I is sufficient

**Option 2:**Only II is sufficient

**Option 3:**Either I or II is sufficient

**Option 4:**Both I and II together are sufficient

**Option 5:**Neither I nor II is sufficient

**Answer:**

**4:**Both I and II together are sufficient

Explanation:

Statement-I

80×40 = 3200

Statement-II

55×30 = 1650

From statement I and statement II:

(3200-1650)/50 = 31 years

Therefore, both statements are required to answer.

**8) In a class with a certain number of students if a teacher weighing 72 kg is added, then average weight of class is increased by 2 kg. If one more teacher weighing 54 kg is added, then the average weight of the class increases by 3 kg over the original average. What is the original average weight (in kg) of the class?**

**Option 1:**50

**Option 2:**30

**Option 3:**20

**Option 4:**60

**Option 5:**40

**Answer:**

**2:**30

**Explanation:**

**Solution:**

**Let the students in a class be x**

**And average weight of class is y**

**According to question,**

(xy+72)/(x+1) = y+2

*xy+72x+1=y+2*⇒

**xy + 72 = xy + 2x + y + 2**

⇒

**2x + y = 70 ……(i)**

**Now, another teacher joined the class**

(xy+72+54)/(x+2) = (y+3)

*xy+72+54x+2=y+3*⇒

**xy + 126 = xy + 3x + 2y + 6**

⇒

**3x + 2y = 120 ….(ii)**

**By equation (i) and (ii)**

**Number of students, x = 20**

**∴**

**Original average weight, y = 30 kg**

**9) In World cup, Virat scored an average of 83 runs per match in the first 3 match and an average of 86 runs per match in the last four matches. What is Virat’s average run for the first match and the last match if his average run per match for all the five matches is 84.8?**

**Option 1:**75

**Option 2:**82

**Option 3:**80

**Option 4:**84

**Option 5:**85

**Answer:**

**2:**82

**Explanation:**

**Solution:**

**I + II + III = 83 × 3 = 249 …… (i)**

**II + III + IV + V = 86 × 4 = 344 …… (ii)**

**I + II + III + IV + V = 84.8 × 5 = 424 ….. (iii)**

**From equation (ii) and (iii)**

**I = 80 …… (iv)**

**Now, From Equation (i), (ii) and (iv)**

**IV + V = 175 …… (v)**

**From equation (i), (iii) and (v)**

**I + V = 164**

**Therefore required average=**

*164/2=82***10) Find the average of all the numbers between 11 and 125 which are divisible by 15?**

Option 1:75

Option 1:

**Option 2:**60

**Option 3:**67.5

**Option 4:**65.5

**Option 5:**68

**Answer:**

**3:**67.5

**Explanation:**

**Multiples are = 15, 30, 45, 60, 75, 90, 105, 120**

**Average = (First term + Last term)/2**

**= (15+120)/2**

**= 67.5**