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1. A' and 'B' complete a work togather in 8 days.If 'A' alone can do it in 12 days.Then how many day 'B' will take to complete the work?
2. Ravi's salary was reduced by 25%.Percentage increase to be effected to bring the salary to the original level is
Answer: 33 1/3 %Explanation:
Let's assume Ravi salary = 100
It get reduced by 25% => Salary = 75
75(1 + P/100) = 100
1+ P/100 = 4/3
P = 100/3 = 33 1/3%.
You can use directly formula i.e
[(R*100)/(100-R)]% Where 'R' is decresed %
so put 25 at place of 'R'
=> [(25 * 100)/(100 - 25)]% => [(25 *100)/75]%
=>100/3% = 33 1/3%
3. A and B can finish a piece of work in 20 days .B and C in 30 days and C and A in 40 days. In how many days will A alone finish the job
Find one day work for all three
(A+B)'s 1 day work = 1/20 ----(1)
(B+C)'s 1 day work = 1/30 ----(2)
and (C+A)'s 1 day work = 1/40 ----(3)
2(A+B+C) 1 day work = (1/20 + 1/30 + 1/40)
=> (A+B+C) = (6+4+3)/2*120
=> (A+B+C) = 13/240 -----------(4)
By eq. (2) and (4)
A + 1/30 = 13/240
=> A = 13/240 - 1/30 = (13-8)/240 = 1/48
then A's 1 day work = 1/48
so A alon can finish the job = 48 days
4. Two trains each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is
Answer: 60 km /hrExplanation:
speed of the faster train = 2x m/sec.
Relative speed of train = (x + 2x) m/sec = 3x m/sec.
Total distance = (100 + 100)m = 200m
3x = 200/8
=> 24x = 200 => x = 25/3
So speed of the faster train = 2 * 25/3 m/sec
= 50/3 m/sec
= 50/3 * 18/5 = 60 km/hr.
5. What is the product of the irrational roots of the equation (2x-1)(2x-3)(2x-5)(2x-7)=9?
6. The total population of a village is 5000. The number of males and females increases by 10% and 15% respectively and consequently the population of the village becomes 5600. what was the number of males in the village ?
Lets Assume males and females as x and y respectively.
So total Population (x+y)=5000 -----------(1)
Incresed by 10% and 15%
By Solving eq. (1) & (2)
y=2000 x=3000 (i.e Male population)
7. A thief steals a car at 2.30 p.m and drives it at 60 kmph. The theft is discovered at 3 p.m and the owner sets off in another car at 75 kmph. When will be overtake the thief.
Answer: 5:00 p.mExplanation:
As Theft is discovered at 3:00pm but Thief stole the car at 2:30.
This means thief covered some distance in this 30 min gap.
Distance travelled by thief in 30 min = 60 * 1/2 = 30 km
Owner Discovered Car at 3:00pm
Now relative speed = (75-60)km/hr = 15km/hr
Time needed to travel 30km by the speed of 15km/hr.
Time at which owner meets thief = 30/15 = 2 hrs
So After 2 hrs (i.e,at 5:00 pm) the owner will catch/overtake the thief
8. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg
1. Given fresh fruit has 68% water,
=> Remaining 32% will be fruit content.
2. Given Dry fruit has 20% water
=> Remaining 80% is fruit content.
Here assume weight of dry fruit = x kg.
"fruit content in both the fresh fruit and dry fruit is the same"
Fruit % in fresh-fruit = fruit% in dry-fruit
so (32/100) * 100 = (80/100 )* x
=> x = 40 kg.
9. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both taps are opened simultaneously, then after how much time will the cistern get filled ?
Answer: 7.2 hoursExplanation:
Time taken by tap A to fill the cistern=4 hrs
so work done by tap A in 1 hour = 1/4th
Time taken by tap B to empty the full cistern = 9 hours
so work done by tap B in 1 hour = 1/9th
=> Work done by (A + B) in 1 hour=(1/4 - 1/9)=5/36
Therefore, the tank will fill the cistern = 36/5 hours=7.2 hours.
10. Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages ?
Answer: 8.15 hoursExplanation:
Number of pages typed by ronald in 1 hour = 32/6 = 16/3.
Number of pages typed by elan in 1 hour = 40/5 = 8.
Number of pages typed by both in 1 hour = (16/3+8) = 40/3.
Time taken by both to type 110 pages = (110*3/40)hrs = 8 1/4hrs = 8 hrs 15 min.