Average,Mixtures Practice test
1.
The average income of A and B is Rs 6000 and that of C,D,E is Rs 8000. The average income of all the 5 people is
A. 7000
B . 7200
C. 7500
D. 8000
Answer: Option B
Explanation:
Average income of all 5= (6000*2 + 8000*3)/5 = 7200
2.
The sum of the ages of Neelima and her father is 62 years. After four years, the age of the father will be four times that of the Neelima.Then the difference between their ages is
A. 30
B. 34
C. 42
D. 41
Answer: Option C
Explanation:
Let Neelima’s present age be x years so that his father’s age be (62 -x) years of age.
⇒ 4 (x + 4) = (62 – x + 4)
⇒ x = 10, so her father’s age = (62 – 10) years = 52 years.
Difference=42
3.
Milk and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3 respectively. In what ratio the liquids in both the vessels should be mixed to obtain a new mixture in vessel C, maintaining half milk and half water?
A. 1 : 1
B. 7 : 5
C. 2 : 4
D. 1 : 3
Answer: Option B
4.
A batsman has a certain average of runs for 25 innings. In the next innings, he scores 156 runs thereby increasing his average by 2 runs. His new average is
A. 100 runs
B. 102 runs
C. 104 runs
D. 106 runs
Answer: Option D
Explanation:
Let the average runs be x, initially
Total runs = 25x
25x+156 = 26(x+2)
x = 156-52 =104
At present his new average = 104 + 2 = 106 runs
5.
Among A, B, C, D, and E, A weighs 2 kg less than B, B weighs 2 kg more than D or E, individually. But C weighs 6 kg more than B. The average weight of these five will be equal to the weight of whom among the following?
A. C
B. B
C. D
D. A
Answer: Option B
Explanation:
A, D, E weighs 2 kg less than B individually. Total 6 kg less. And C is 6 kg more than B. So the difference is cancelled. So B’s weight is equal to the average weight.
6.
The average weekly salary per head of the entire staff of a factory consisting of supervisors and the laborers is Rs 60.The average salary per head of the supervisors is Rs 400 and that of the laborers is Rs 56.Given that the number of supervisors is 12.Find the number of laborers in the factory.
A. 1020
B. 1130
C. 1010
D. 1240
Answer: Option A
Explanation:
Average salary of laborer Rs 56
Average salary of supervisors Rs 400
Average salary of entire staff Rs 60 340: 4
Number of laborer / Number of Supervisors = 340 / 4=85/1
Thus,if the number of supervisors is 1,number of laborers =85.
Therefore if the number of supervisors is 12 number of laborers
85*12=1020.
7.
How many Kilograms of Pure water is to be added to 100 Kilograms of a 30% saline solution to make it a 10% saline solution?
A. 150 Kilograms
B. 100 Kilograms
C. 250 Kilograms
D. 200 Kilograms
Answer: Option D
Explanation:
Let x be the weights, in Kilograms, of pure water to be added. Let y be the weight, in Kilograms, of the 10% solution.
Hence X + 100 = y
Let us now express the fact that the amount of salt in the pure water (which 0) plus the amount of salt in the 30% solution is equal to the amount of salt in the final saline solution at 10%.
0 + 30% 100 = 10% y
Substitute y by x + 100 in the last equation and solve.
30% 100 = 10% (x + 100)
Solve for x.
X = 200 Kilograms.
8.
A man spends Rs. 750 on an average during first 8 months. During the next 4 months he spends Rs. 680 per month. He took loan of Rs. 320 during the year and paid Rs. 600 for LIC premium. Find his monthly average income?
A. Rs. 650
B. Rs.750
C. Rs. 850
D. Rs.900
Answer: Option B
Explanation:
Total Expenditure – Loan taken = Monthly Income
Expenditure for First 8 months = 6000 (750 x 8)
Expenditure for next 4 months = 2720 (680 x 4)
LIC premium paid = 600
Total Expenditure on a year = 9320.00
Month’s average expenditure = 9320 / 12 = 776.66
Loan taken a year = 320
Months average = 320/12 = 26.66
∴Monthly average income = 776.66 – 26.66 = 750.00
9.
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
A. 8, 20, 28
B. 16, 28, 36
C. 20, 35, 45
D. None of these
Answer: Option B
Explanation:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x – 8) + (7x – 8) + (9x – 8) = 56
20x = 80
x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
10.
5Kg of rice at Rs 6 per Kg is mixed with 4 Kg of rice to get a mixture costing Rs 7 per Kg. Find the price of the costlier rice?
A. 8.25
B. 7.25
C. 8
D. 9.25
Answer: Option A
Explanation:
Using the cross method:
rice at Rs 6 per Kg rice at Rs x per Kg
Mean price Rs 7 per Kg
5 4
x-7:1=5:4
4x-28 = 5
4x=33=>x=Rs 8.25.
Therefore price of costlier rice is Rs 8.25 per Kg