# Mixed Quantitative Aptitude Questions Set 68

1. Out of three numbers, the first is four times the second and is one third of the third. If the average of the three numbers is 221, what will be the second number?
46
42
34
39
None
Option D
Solution:
Let 1st no be x.
(x+x/4+3x) /3=221
(4x+x+12x)/4=221*3
17x/4=221*3
x=13*3*4
x=156.
Second no=156/4=39.
2. If A and B working separately can do a piece of work in 8 and 12 hours respectively. If they work alternatively every hour starting with A at 11 a.m., when will be the work completed?
7pm
8.30pm
6pm
6.30pm
None
Option B
Solution:
A………. 8…… 3
B………. 12……. 2 ….. LCM=24
Alternate 2hrs 5 unit completed
8hrs=20unit completed.
9th hour=A complete 3 unit
Remaining 1/2hrs by B.
At 8.30pm the work completed.
3. In how many different ways can the letters of the word ‘ALLOY’ be arranged?
55
60
45
68
None
Option B
Solution:
No of ways=5!/
=60.
4. 80% of a smaller number is 4 less than 40% of a larger number. The larger number is 85 greater than the smaller one. The sum of these two number is
152
189
235
246
None
Option C
Solution:
Let the smaller number be x and larger number be y.
80% of x + 4 = 40% of y
4y – 8x = 40
y – 2x = 10 ——— (1)
y – x = 85 ———– (2)
Solving equation
x = 75
y = 160
x + y = 235.
5. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a post. If the length of each train be 120 metres, in what time will they cross each other travelling in opposite direction?
15sec
12sec
20sec
10sec
None
Option B
Solution:
Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train =120/15= 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Time =(120 + 120)/20 = 12 sec.
6. A container contains 30 litres of milk. From this container 3 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
21.87litre
23.55litre
24litre
22litre
None
Option A
Solution:
Amount of milk left after 3 repeated process=[30(1-3/30)3] =30*9/10*9/10*9/10
=21.87litre.
7. Ten identical particles are moving randomly inside a closed box. What is the probability that at any given point of time all the ten particles will be lying in the same half of the box?
1/512
2/216
1/326
2/158
None
Option A
Solution:
Probability of a particle lying in any particular half=1/2
Probability of all 10 particles lying in either 1st half or 2nd half
=(1/2)10+ (1/2)10
=1/29
=1/512.
8. P is as much older than Q as he is younger than R. If the sum of the ages of Q and R is 60 years, what is the difference between R and P’s age?
20
25
14
None
Option D
Solution:
9. Two trains starting at the same time from two stations 250 km apart and going in opposite directions cross each other at a distance of 140 km from one of the stations. The ratio of their speeds is
13:9
9:7
7:5
14:11
None
Option D
Solution:
Let the speed of the train =xkm/hr and another tain=ykm/hr.
140/x : (250-140)/y
140/x : 110/y
x:y= 14:11.
10. The percentage profit earned by selling an article for Rs. 2120 is equal to the percentage loss incurred by selling the same article for Rs. 1460. At what price should the article be sold to make 30% profit?
Rs1755
Rs2327
Rs1945
Rs2125
None
Option B
Solution:
Profit %ge = loss %ge
Then CP 2120+1460=3580
=3580/2=Rs1790.
100….. 1790
130 .. ? ==>Rs2327.