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Average - 1

Description: Number of Questions is 15 Each Question carry 1 mark Negative Marking is 0.25
Number of Questions: 15
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Tags: SSC GRE GMAT CAT Arithmetic Average
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If 25 persons went to a Barbeque Nation for a combined dinner party and 10 of them spent Rs. 84 each on their dinner and the rest spent Rs. 4 more than the average expenditure of all the 25, then what was the approximate total money spent by them?

  1. Rs. 90

  2. Rs. 2250

  3. Rs. 2225

  4. Rs. 2100

  5. Rs. 1500


Correct Option: B
Explanation:

Assume x is the average expenditure of 25 people. Then, 25*x = 10*84 + 15 (x + 4)  10*x = 900; x = 90. Thus the total expenditure is 90*25 = 2250.

The average marks of 28 students in math were 50. When 8 students left the school, then the average increased by 5. What is the average of marks obtained by the students who left?

  1. 37.5

  2. 12.5

  3. 17.5

  4. 39.3

  5. 300


Correct Option: A
Explanation:

Total marks of 28 students is 28*50 = 1400. After leaving of 8 students total marks is 20*55 = 1100. Decrease in total marks is 1400-1100 = 300. This decrement is the total marks of 8 students who left the class. Thus average is 300/8 = 37.5

The average weight of 3 persons Kora, Tanzin and Zuko is 90 kg. Another man Bumi joins the group and the average now becomes 85 kg. If another man Marko, whose weight is 3 kg more than that of Bumi, replaces Kora then the average weight of Tanzin, Zuko, Bumi and Marko becomes 81 kg. The weight of Kora is

  1. 99 kg

  2. 85 kg

  3. 94 kg

  4. 82 kg

  5. 89 kg


Correct Option: E
Explanation:

The decrease in the average of three persons is 90 – 85 = 5 kg. Total decrease for three persons is 5 × 3 = 15 kg. The weight of Bumi must be New average – Decrease i.e. 85 – 15 = 70 kg. Marko is weight is 3 kg more i.e. 73 kg replaces Kora and thus the average becomes 81. Now if you compare the four persons with Marko the average decreases by 4, thus the total decrease is 4 × 4 = 16 kg. The new included person Marko must be 16 kg lighter than the person who is excluded i.e. Kora. Thus weight of A is 73 + 16 = 89 kg.

Three years ago, the average age of Katara, Kaya and Dazna was 30 years and that of Kaya and Dazna, 7 years ago, was 20 years. What is Katara’s present age?

  1. 46 years

  2. 5 years

  3. 40 years

  4. Cannot be determined

  5. 45 years


Correct Option: E
Explanation:

Total 3 years ago was 30 × 3 = 90, the present total must be 90 + 9 = 99 years. The total of Kaya and Daznza 7 years ago was 20 × 2 = 40, the present total age of Kaya and Dazna must be 40 + 14 = 54 years. The present age of Katara is 45 years

The average age of a class of 61 students was 18 years 4 months on 1st August. If Sakura, whose age was 19 years 2 months on 1st December, left the school in December, what would be the average age of the class on the following 1st April?

  1. 18 years, 11 months and 27 days

  2. 19 years and 29 days

  3. 18 years, 11 months, 27 days and 21 hours

  4. 18 years, 10 months and 27 days

  5. 18 years, 11 months and 28 days


Correct Option: A
Explanation:

Let us assume all the students are there only up to the following April. Their average would have increased by 8 months (August – March) and would have become 19 years.
  On the other hand, the students who left in the October would have been of age 19 years and 6 months (December – March) on 1st April. This means extra 6 months would decrease the average of all. Now these six month time means 180 days, which would be equally reducing the average of all the 60 students by 180/60 = 3 days.  The real average of the class will be 19 years – 3 days = 18 years + 11 months + 27 days

A stealth jet can fly at 240 kmph in the stratosphere and at 200 kmph in the troposphere. Find its average speed if it is in the troposphere for three quarters of the distance.

  1. 208.6 kmph

  2. 220 kmph

  3. 228.5 kmph

  4. 210 kmph

  5. Can’t be determined


Correct Option: A
Explanation:

Average speed = (Total Distance)/(Time Taken); D/(3D/(4*200) + D/(4*240)) = 208.6

The sum of 4 consecutive two-digit natural numbers, when divided by 10, becomes a perfect square. What is the least possible value of the largest of the four numbers?

  1. 5.5

  2. 93

  3. 13

  4. Can’t be determined

  5. 163


Correct Option: C
Explanation:

Let the 4 consecutive odd numbers be x - 3, x - 1, x + 1 and x + 3. Sum of these numbers is 4x. √4x/10 or 2√x/10 is a perfect square. Now take different values of x. At x = 10, it becomes a perfect square. So, the four numbers are 7, 9, 11 and 13.

Hinata and Saske were married 7 years ago. The average age of Hinata and Saske was 25 years when they were married. At present, the average age of Hinata, Saske and their child is 22 years. How many years after their marriage was the child born?

  1. 3 years

  2. 2 years

  3. 5 years

  4. 8 years

  5. 6 years


Correct Option: C
Explanation:

(Hinata + Saske)/2 = 25 (7 years ago) Their total age 7 years ago = 50 years Hence, their total present age = 50 + 7 + 7 = 64 years Total age of their family (Hinata + Saske + Child) = 22 * 3 = 66 years Age of child = 66 – 64 = 2 years. Hence, child was born 7 – 2 = 5 years after marriage.

What is the average of first n whole numbers?

  1. (n - 1)/2

  2. (n + 1)/2

  3. n/2

  4. data inadequate

  5. n/3


Correct Option: A
Explanation:

Whole numbers start from 0; hence n whole numbers means n-1 natural numbers. Sum first n-1 natural numbers is {(n-1)(n-1+1)}/2 ; Average is ((n-1)*n)/(2*n) , Average is (n-1)/2.

Naruto buys rice worth Rs. 1,34,650. On the way, 60% of the rice gets damaged. He is forced to sell it at a loss of 20%. At what profit percentage should he sell the remaining rice to have an average overall profit of 20%?

  1. 95% profit

  2. 80% profit

  3. 330% profit

  4. 20% profit

  5. 170% profit


Correct Option: B
Explanation:

Worth of rice which is damaged = 60/100*134650 = 80790. Its selling price is 80790*.8 = 64632. Total selling price should be 134650*1.2 = 161580. Remaining rice is sold at 161850 - 64632 = Rs. 97218 to get overall 20% profit. So, profit is (96948 - 53860)/53860*100 = 80% (approximately).

The average salary of 30 officers in a firm is Rs. 120 and the average salary of laborers is Rs. 40. Find the total number of employees, if the average salary of the firm is Rs. 50.

  1. 210

  2. 240

  3. 220

  4. 390

  5. 83


Correct Option: B
Explanation:

Let the total number of laborers be x. (120*30 + 40*x)/(30 + x) = 50; x = 210. Hence, total number of employees is 210 + 30 = 240.

The average age of Daffny, Kirito and Kakashi is 55. Daffny’s age is as much more than the average as Kirito’s age is less than the average. Find the age of Kakashi.

  1. 45 years

  2. 110 years

  3. 65 years

  4. 55 years

  5. Cannot be determined


Correct Option: D
Explanation:

(Daffny + Kirito + Kakashi)/3 = 55. Daffny – 55 = 55 – Kirito, Daffny + Kirito = 110. Their total age is 165 and hence, Kakashi’s age is 55.

There are 137 consecutive odd integers. The average of the first 129 is n. What is the average of all 137?

  1. n + 4

  2. n + 8

  3. n + 6

  4. n + 10

  5. Cannot be determined


Correct Option: B
Explanation:

Average of consecutive integers is always middle term. So, the average of first 129 terms is (129 + 1)/2= 65th term, which is n. Average of 137 terms is (137 + 1)/2 = 69th term. So, 69th term is 65th term + 2*4 = n + 8.

Eleven years ago, the ages of the members of a family of six people added up to 205 years. Three years later, one member died at the age of 55 years and a child was born during the same year. After another three years, one more member died, again at 55, and a child was born during the same year. The current average age of this six-member family is nearest to

  1. 23 years

  2. 45 years

  3. 24 years

  4. 27 years

  5. 26 years


Correct Option: D
Explanation:

11 years ago, age of 6 members = 205  3 years later, total age of 6 members = 205 + 6*3 - 55 = 168 After another 3 years, total age of 6 members = 168 + 6*3 - 55 = 131 Current total age of 6 members = 131 + 5*6 = 161 Thus, the average is 161/6 = 27 (approximately)

The average marks of a class of 50 students were calculated to be 64.15. It was later discovered that the marks of a student were taken to be 39, instead of 75. Find the real average of the class.

  1. 64.87

  2. 65.07

  3. 64.89

  4. 64.99

  5. 64.97


Correct Option: A
Explanation:

 By taking 75 instead of 39, total increment is 36. These 36 marks are equally distributed in all 50 students. Hence. marks of each student are increased by 0.72. Hence, average becomes 64.15 + 0.72 = 64.87.

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