Direction (Q. 1-5) : In each of these questions, two equations (I) and (II) are given. You have to solve both equations and give answer :
1) If x < y
2) If x > y
3) If x = y or no relationship can be established between x and y.
4) If x >= y
5) If x <= y
1.
I. x^2 = 1/4
2.
I. 3x^2 + 11x - 4 = 0
II. y^2 - 5y + 6 = 0
3.
I. x^2 + 12x + 35 = 0
II. y^2 + 15y + 56 = 0
4.
I. x^2 – x – 6 = 0
II. y^2 + 3y – 4 = 0
5.
I. x^2 - 7x + 12 = 0
II. y^2 - 11y + 30 = 0
Directions (Q. 6-7) : Study the information given below and answer the questions carefully :
Ramesh, Dinesh and Ganesh completed a job in 12 days. They worked together for 4 days in which they completed 44% of the total work. But due to unavoidable circumstances Ramesh quits the job at this point. Work done by Dinesh in 3 days is equal to the work done by Ganesh in 4 days.
6. Find the time taken by the fastest worker to complete the job.
1) 21.875 days
2) 23.475 days
3) 18.245 days
4) 17.465 days
5) None of these
7. Find by what per cent the slowest worker is less efficient than the second fastest worker?
1) 13.54%
2) 12.5%
3) 37.5%
4) 44%
5) None of these
8. Tap A fills a tank with water in 10 hrs. Tap B fills the same tank with milk in 12.5 hrs. A man who wanted to fill the tank with the mixture starts tap A first in a tank, which already contains 8% milk of its own capacity. After two hours he also starts tap B till the tank gets filled completely. In what proportion should he mix this solution with the other one containing water and milk in the ratio 2 : 3, so that the new solution will contain half milk and half water?
1) 4 : 5
2) 5 : 4
3) 3 : 7
4) 14 : 15
5) None of these
9. With the help of the digits 1, 2, 3 and 4 find the sum of all 4 – digits numbers provided that the digits are not repeated.
1) 66,660
2) 6500
3) 40375
4) 100013
5) None of these
10. The sides of a triangle are in the ratio of 1/2 : 1/3 : 1/4. If the perimeter is 52cm, then the length of the smallest side is
1) 9 cm
2) 10 cm
3) 11 cm
4) 12 cm
5) None of these
Answers:
1. 5
2. 2
3. 4
4. 3
5. 4
6. 1
Since the ratio of no. of days taken by Dinesh and Ganesh
= 3 : 4
ED : EG = 4 : 3,
Since the total efficiency of Dinesh and Ganesh is (4 + 3 = 7) and with this efficiency they complete remaining work after 4 days ( 100%–44%=56 %) in 8 days. It means they did 8% work per day.
7 efficiency = 8 days 56% work
7 efficiency = 1 day 8% work
In first 4 days total work by Dinesh and Ganesh is 32%.
Therefore Ramesh must have done 44% – 32% = 12% in 4 days.
So in 1 day he does 3% work.
So total work he will do in 33 1/3 days
Further, 7E -----> 8% of total work
1 E -----> 8/7 % of total work
3 E (Ganesh) -----> 24/7% of total work
Time taken by Ganesh to finish the work alone = 100*7/24 = 87.5/3 days
and 4E (Dinesh) -----> 8/7 4% of total work = 32/7% of total work
Time taken by Dinesh to finish the whole work alone
= 87.5/4 days
Ramesh -----> 100/3 days(Slowest)
Dinesh -----> 87.5/4= 21.875 days (Fastest)
Ganesh -----> 87.5/3 (Second fastest).
Therefore option 1 is
correct.
7. 2;
DR : DG = 100/3 : 87.5/3
ER : EG = 87.5 : 100
Required ratio = ER : EG = 7 : 8
Thus less efficiency = 1/8 * 100 = 12.5%
8. 5; The ratio of water and milk in the tank according to the proceeding is (20% + 40%) : (8% + 32%).(In first 2 hours water will be restored in tank by 20% and in next 4 hrs.40% more, and milk as per calculation 100%, in 12.5 hrs.
So in 1hr only 8% of whole tank will be filled up. Therefore in 4 hrs 32% of whole tank is filled up.)
So present ratio of water to milk = 3 : 2
And the second ratio of water to milk = 2 : 3
As per allegation rule =
Hence option (5) is correct.
9. 1;
1 × 2 × 3 × 4 = 24 numbers, it mean at every place digits
will occur six times.
Sum of one column = 6 ( 1 + 2 + 3 + 4) = 60
Hence, sum of all the numbers
= 60 × (100 + 101 + 102 + 103)
= 60 × 1111 = 66660
10. 4
Ratio of sides of the triangle = 1/2 : 1/3 : 1/4 = 6: 4: 3
Let the sides be 6k, 4k and 3k respectively.
13 K = 52
K = 4
Sides are 24 cm, 16cm and 12cm.