2. Average weight of three friends Amar, Visera and Daman is 70 kg. Another person Vishal joins the group and now the average is 66 kg. If another person Tahir whose weight is 6 kg more than Vishal, joins the group replacing Amar, then average weight of Visera, Daman, Vishal and Tahir becomes 75 kg. What is the weight of Amar (in kg)?
3. The average salary of a company increases by 100 when the salary of the manager, which is Rs. 9500, is included. If the number of employees excluding the manager is the smallest cube divisible by 16, what is the final average of the company?
4. An exam was conducted in a state over 222 centres. The average number of applicants per centre was found to be 1560. However, it was later realized that in one centre, the number of applicants was counted as 1857 instead of 1747. What was the correct average number of applicants per centre (upto two decimals)?
5. In Champions league, Rohit scored an average of 120 runs per match in the first 3 match and an average of 140 runs per match in the last four match. What is Rohit’s average runs for the first match and the last two match if his average runs per match for all the five match is 122 and total number of matches are 5?
Answer & Explanation:
1. Answer: Option C
Explanation:
Total score of 40 students = (40 x 76) = 3040
Total score of top 3 scorers = 3040 – (37 x 75) = 265
To minimize the score of the top scorer, we assume the other two top scorers score the maximum they can = 85 marks each.
So, the top scorer scored = 265 – 170 = 95 marks.
2. Answer: Option D
Explanation:
Total weight of Amar, Visera and Daman = 70 x 3 = 210 kg
Again, Amar + Visera + Daman + Vishal = 66 x 4 = 264 kg ……… (i)
Weight of Vishal = 264 – 210 = 54 kg
Weight of Tahir = 54 + 6 = 60 kg
Now, as per the question
Visera + Daman + Vishal + Tahir = 75 x 4 = 300 kg. ………………. (ii)
Subtracting (i) from (ii), we get
Tahir – Amar = 60 – Amar = 300 – 264 = 36
Therefore, weight of Amar = 60 – 36 = 24 kg
3. Answer: Option D
Explanation:
The smallest cube divisible by 16 is 64.
Lets assume the average salary before the manager’s salary is included is x
After addition of Manager’s salary the average increases by 100
We can write down the above information in form of an equation as:
64x + 9500 = 65 × (x + 100)
Solving for x, we get x = 3000
The final average is 3000 + 100 = Rs. 3100
4. Answer: Option D
Explanation:
Number of applicants that have been counted extra = 1857 − 1747 = 110
Hence, decrease in average = \(\frac{110}{222}\) = 0.495
Correct average = 1560 − 0.495 = 1559.505 = 1559.51
5. Answer: Option A
Explanation:
Rohit’s average score in the first 3 exams = 120
Let the scores in the 5 exams be denoted by M1, M2, M3, M4, and M5
M1 + M2 + M3 = 120 × 3 = 360 …….(i)
Average of last 4 match = 140
\(\frac{M2 + M3 + M4 + M5}{4}\)= 140
M2 + M3 + M4 + M5 = 560 ……(ii)
Average of all the exams
\(\frac{M1 + M2 + M3 + M4 + M5}{5}\)=122
M1 + M2 + M3 + M4 + M5 = 122 × 5 = 610 …….(iii)
From solving above equation, we get M1 + M4 + M5 = 300
Required average runs =\(\frac{300}{3}\)= 100
2. While purchasing an item that costs Rs. 400, one has to pay sales tax at the rate of 7% and on another item costing Rs. 6400, the rate of sales tax was 9%. The percent of sales tax one has to pay, taking these items together on an average is?
3. The average salary of male employees in a firm was Rs. 6000 and that of females was Rs. 5600. The mean salary of all the employees was Rs. 5800. What is the % of female employees?
4. The average salary of 65 workers is Rs. 5680 out of which average salary of 31 workers is Rs. 2356 and that of 23 workers is Rs. 4589. What is the average salary of remaining workers?(value in approximate)
5. The average sales of a mobile shopkeeper was 15 mobiles per week, to increase the sales he decided to tie up with a finance company for providing mobiles to customers on installment. After the launch of this scheme his average sales increased to 21 mobile per week. The annual percentage increase in the sales of mobile was:
Answer & Explanation:
1. Answer: Option D
Explanation:
Let x be the number of students in the class and y be the average weight of the class
Now according to question,
\(\frac{xy + 50}{x + 1}\)= y + 1
x + y = 49 ………. (i) Again,
\(\frac{xy + 50 + 50}{x + 2}\)= y + 1.5
1.5x + 2y = 97 ………. (ii) From equation (i) and (ii), we get y = 47
2. Answer: Option D
Explanation:
Sales tax on the article sold at Rs. 400 = \(\frac{400 × 7}{100}\)= 28
Sales tax on the article sold at Rs. 6400= \(\frac{6400 × 9}{100}\)= 576
Total tax = 28 + 576 = 604
Percentage sales tax = \(\frac{604}{6800}\)x100 = 8\(\frac{15}{17}\)%
3. Answer: Option B
Explanation:
Average salary of male employees = Rs. 6000
Average salary of female employees = Rs. 5600
Mean salary = Rs. 5800
The ratio of male : female = 200 : 200 = 1 : 1
Hence, % of female employees = \(\frac{1}{2}\)x100 = 50%
4. Answer: Option C
Explanation:
Total salary of 65 workers = 65 × 5680 = Rs. 369200
Total salary of 31 workers = 31 × 2356 = Rs. 73036
Total salary of 23 workers = 23 × 4589 = Rs. 105547
No. of remaining workers = 65 – 31 – 23 = 65 – 54 = 11
Total Salary of 11 workers = 369200 – 73036 – 105547 = 369200 – 178583 = Rs. 190617
Required average =\(\frac{190617}{11}\)=17329(approx)
5. Answer: Option A
Explanation:
The average rate of percentage increase in both the cases- weekly and yearly will be the same.
Therefore, annual percentage in sales = \(\frac{21 – 15}{15}\)x100= 40%
2. The average age of A and B is 20 years. If A is to be replaced by C, the average would be 19 years. The average age of C and A is 21 years. The ages of A, B and C in order (in years) are
3. The average monthly income of a family of four earning members was Rs. 15130. One of the daughters in the family got married and left home, so the average monthly income of the family came down to Rs. 14660. What is the monthly income of the married daughter ?
4. A man purchases milk for three consecutive years. In the first year, he purchases milk at the rate of Rs. 7.50 per litre, in the second year, at the rate of Rs. 8.00 per litre and in the third year, at Rs. 8.50 per litre. If he purchases milk worth Rs. 4,080 each year, the average price of milk per litre for the three years is
5. The average weight of 21 boys was recorded as 64 kg. If the weight of the teacher was added, the average increased by one kg. What was the teacher’s weight ?
Answer & Explanation:
1. Answer: Option C
Explanation:
Maximum average could be
\(\frac{(10 + 10 + 10 + 10 + 10 + 10 + 5)}{7}\)= 9.28
Which is being satisfied by option C i.e. 9.42.
2. Answer: Option C
Explanation:
A + B = 2 × 20 = 40 yr
B + C = 2 × 19 = 38 yr
C + A = 2 × 21 = 42 yr
On adding all three,
2 (A + B + C) = 40 + 38 + 42 = 120
⇒ A + B + C = 60
A = (A + B + C) – (B + C) = 60 – 38 = 22 yr
Similarly,
B = (A + B) – A = 40 – 22 = 18 yr
C = (C + A) – A = 42 – 22 = 20 yr
3. Answer: Option C
Explanation:
Total monthly income of 4 members = 15130 × 4 = Rs. 60520
Except daughter, total monthly income of 3 members = 14660 × 3 = Rs. 43980
Monthly income of married daughter = 60520 – 43980 = Rs. 16540
4. Answer: Option B
Explanation:
Price of milk in first year = Rs. 7.50 per litre.
Quantity of milk in first year =\(\frac{4080}{7.50}\)= 544 liters
Price of milk in second year = Rs. 8.00 per litre.
Quantity of milk in second year = \(\frac{4080}{8.00}\)= 510liters
Price of milk in third year = Rs. 8.50 per litre.
Quantity of milk in third year =\(\frac{4080}{8.50}\)= 480 liters
Required average = \(\frac{3 * 4080}{544 + 510 + 480}\)= Rs. 7.98
5. Answer: Option A
Explanation:
Total weight of 21 boys = 64 x 21 = 1344 kg
Given that if the weight of the teacher was added, the average increased by one kg
Total weight along with the teacher = 65 x 22 = 1430 kg
Now, teacher’s weight = 1430 – 1344 = 86
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