EQUATIONS AND INEQUATIONS - I

Directions (1-5): For the two given equations I and II.

Give answer (1) if p is greater than q.

Give answer (2) if p is smaller than q.

Give answer (3) if p is equal to q.

Give answer (4) if p is either equal to or greater than q.

Give answer (5) if p is either equal to or smaller than q.

1. I. p^2 + 5p + 6 = 0 and II. q^2 + 3q + 2 = 0

2. I. p^2 = 4 and II. q^2 + 4q = - 4

3. I. p^2 + p = 56 and II. q^2 - 17q + 72 = 0

4. I. 3p + 2q - 58 = 0 and II. 4q + 4p = 92

5. I. 3p^2 + 17p + 10 = 0 and II. 10q^2 + 9q + 2 = 0

Directions (6-10): In each of the following questions two equations are given. You have to solve the equations and
Give answer (1) if x < y
Give answer (2) if x <= y
Give answer (3) if x = y
Give answer (4) if x >= y
Give answer (5) if x > y

6. I. 4x^2 - 8x + 3 = 0 and II. 2y^2 - 7y + 6 = 0
7. I. x^2 + x - 6 = 0 and II. 2y^2- 13y + 21 = 0
8. I. x^2 - x - 6 = 0 and II. 2y^2 + 13y + 21 = 0
9. I. x^2 = 4 and II. y^2 + 6y + 9 = 0
10. I. 2x + 3y = 4 and II. 3x + 2y = 11

Directions (11-15): In each of the following questions two equations I and II are given. You
have to solve both the equations and - Give answer if
(1) x > y
(2) x <= y
(3) x < y
(4) x >= y
(5) x = y or relationship between x and y cannot be established

11. I. 4x + 2y = 51 and II. 15y + 13x = 221
12. I. 8x^2 + 3x = 38 and II. 6y^2 + 34 = 29y
13. I. x^2 + 91 = 20x and II. 10y^2 - 29y + 21 = 0
14. I. 6x^2 + 13x + 5 = 0 and II. 9y^2 + 22y + 8 = 0
15. I. (x + y)^2 = 784 and II. 92551 = 92567 - y

16. If 4x + 5y = 83 and 3x/2y = 21/22 then what is the value of y - x ?
(1) 3
(2) 4
(3) 7
(4) 11
(5) None of these

Directions (17-21): In the following questions two equations numbered I and II are given. You have to solve both the equations and
Give answer (1) if x > y
Give answer (2) if x >= y
Give answer (3) if x < y
Give answer (4) if x <= y
Give answer (5) if x = y or the relationship cannot be established

17. I. x^2 - 14x + 48 = 0 and II. y^2 + 6 = 5y
18. I. x^2 + 9x + 20 = 0 and II. y^2 + 7y + 12 = 0
19. I. x^2 = 529 and II. y = √529
20. I. x^2 + 13x = - 42 and II. y^2 + 16y + 63 = 0
21. I. 2x + 3y = 14 and II. 4x + 2y = 16

22. If 3y + 9x = 54 and 28x/13y = 140/39 then what is the value of y - x ?
(1) -1
(2) -2
(3) 2
(4) 1
(5) None of these

Mixture and Allegation Previous Years -II

1. Several litres of acid were drawn off a 54 L vessel full of acid and an equal amount of water added, Again, the same volume of the mixture was drawn off and replaced by water. As a result the vessel contained 24 L of pure acid. How much of the acid was drawn off initially ?
(1) 12 L
(2) 16 L
(3) 18 L
(4) 24 L
(5) None of these

2. 37.85% and 92% alcoholic solutions are mixed to get 35 L of an 89% alcoholic solution. How many litres of each solution are there in the new mixture ?
(1) 10 of the first and 25 of the second
(2) 20 of the first and 15 of the second
(3) 15 of the first and 20 of the second
(4) None of the above
(5) Cannot Be Determined

3. Three containers, A, B and C are having mixtures of milk and water in the ratio 1 : 5, 3 : 5 and 5 : 7 respectively. If the capacities of the containers are in the ratio 5 : 4 : 5, then find the ratio of the milk to the water, if the mixtures of all the three containers are mixed together.
(1) 51 : 115
(2) 52 : 115
(3) 53 : 115
(4) 54 : 115
(5) None of these

4. A chemist has 10 L of a solution that is 10% nitric acid by volume. He wants to dilute the solution to 40% strength by adding water. How many litres of water must be add ?
(1) 15
(2) 20
(3) 18
(4) 25
(5) None of these

5. 5 L of water is added to a certain quantity of pure milk costing Rs 3/L. If by selling the mixture at the same price as before, a profit of 20% is made, then what is the amount of pure milk in the mixture ?
(1) 20 L
(2) 30 L
(3) 25 L
(4) 35 L
(5) None of these

6. How many kg of sugar costing Rs 5.75 per kg should be mixed with 75 kg of cheaper sugar costing Rs 4.50 per kg so that the mixture is worth Rs 5.50 per kg ?
(1) 350 kg
(2) 300 kg
(3) 250 kg
(4) 325 kg
(5) None of these

7. The amount of water (in ml.) that should be added to reduce 9 mL lotion, containing50% alcohol, to a lotion containing 30% alcohol is :
(1) 5 mL
(2) 4 mL
(3) 3 mL
(4) 6 mL
(5) None of these

8. A person has a chemical of Rs 25 per litre. In what ratio should water be mixed in that chemical, so that after selling the mixture at Rs 20 per litre he may get a profit of 25% ?
(1) 13 : 16
(2) 12 : 15
(3) 16 : 9
(4) 19 : 22
(5) None of these

9. 50 g of an alloy of gold and silver contains 80% gold (by weight). The quantity of gold, that is to be mixed up with this alloy, so that it may contain 95% gold, is
(1) 200 g
(2) 50 g
(3) 150 g
(4) 10 g
(5) None of these

10. A bottle contains 3/4 of milk and the rest water. How much of the mixture must be taken away and replaced by an equal quantity of water so that the mixture has half milk and half water ?
(1) 25%
(2) 33(1/3)%
(3) 45%
(4) 50%
(5) None of these


Answers :)

Mixture and Allegation Previous Years -I

1. In a mixture of milk and water the proportion of water by weight was 75%. If in the 60 gms mixture 15 gms water was added, what would be the percentage of water in the new mixture ?
(1) 75%
(2) 88%
(3) 90%
(4) 100%
(5) None of these

2. In 1kg mixture of sand and iron, 20% is iron. How much sand should be added, so that the proportion of iron becomes 5% ?
(1) 3 kg
(2) 4 gms
(3) 5 gms
(4) 6 kg
(5) None of these

3. The wheat sold by a grocer contained 10% low quality wheat. What quantity of good quality wheat should be added to 150 kgs of wheat so that the percentage of low quality wheat becomes 5% ?
(1) 150 kgs
(2) 135 kgs
(3) 50 kgs
(4) 85 kgs
(5) None of these

4. A grocer purchased 2 kg. of rice at the rate of Rs. 15 per kg. and 3 kg. of rice at the rate of Rs. 13 per kg. At what price per kg should he sell the mixture to earn 33(1/3)% profit on the cost price ?
(1) Rs. 28.00
(2) Rs. 20.00
(3) Rs. 18.40
(4) Rs. 17.40
(5) None of these

5. Two barrels contain a mixture of ethanol and gasoline. The content of the ethanol is 60% in the first barrel and 30% in the second barrel. In what ratio must the mixtures from the first and the second barrels be taken to form a mixture containing 50% ethanol ?
(1) 1 : 2
(2) 2 : 1
(3) 2 : 3
(4) 3 : 2
(5) None of these

6. To x litres of an x% solution of acid, y litres of water is added to get (x -10)% solution of acid. If x > 20, then value of y is
(1) x^2/100
(2) 10x/x-10
(3) 10/x+10
(4) 10x^2/x-10
(5) None of these

7. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be :
(1) 5 : 7
(2) 5 : 9
(3) 7 : 5
(4) 9 : 5
(5) None of these

8. A container has 30 litres of water. If 3 litres of water is replaced by 3 litres of spirit and this operation is repeated twice, what will be the quantity of water in the new mixture ?
(1) 24 litres
(2) 23 litres
(3) 24.3 litres
(4) 23.3 litres
(5) None of these

Answers :)
1. 5
2. 1
3. 1
4. 3
5. 2
6. 2
7. 3
8. 3

Time and Work Previous Years -II

1. Three men, four women and six children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days ?
(1) 8
(2) 7
(3) 12
(4) Cannot be determined
(5) None of these

2. 12 men take 36 days to do a work while 12 women complete 3/4 th of the same work in 36 days. In how many days 10 men and 8 women together will complete the same work ?
(1) 6
(2) 27
(3)12
(4) Data inadequate
(5) None of these

3. ‘A’ can complete a piece of work in 12 days. ‘A’ and ‘B’ together can complete the same piece of work in 8 days. In how many days can ‘B’ alone complete the same piece of work ?
(1) 15 days
(2) 18 days
(3) 24 days
(4) 28 days
(5) None of these

4. 12 men can do a piece of work in 10 days. How many men would be required to do the same work in 8 days ?
(1) 14
(2) 18
(3) 16
(4) 12
(5) None of these

5. A and B together complete a piece of work in T days. If A alone completes the work in T +3 days and B alone completes the piece of work in T +12 days, what is T ?
(1) 3 days
(2) 12 days
(3) 9 days
(4) Cannot be determined
(5) None of these

6. 4 men can complete a piece of work in 2 days. 4 women can complete the same piece of work in 4 days whereas 5 children can complete the same piece of work in 4 days. If 2 men, 4 women and 10 children work together, in how many days can the work be completed ?
(1) 1 day
(2) 3 days
(3) 2 days
(4) 4 days
(5) None of these

7. Amit and Sujit together can complete an assignment of data entry in 5 days. Sujit’s speed is 80% of Amit’s speed and the total key depressions in the assignment are 5,76,000. What is Amit’s speed in key depressions per hour if they work for 8 hours a day ?
(1) 4800
(2) 6400
(3) 8000
(4) 7200
(5) None of these

8. 9 Men working for 7 hours a day can complete a piece of work in 15 days. In how many days can 6 men working for 9 hours a day, complete the same piece of work ?
(1) 17(1/2) days
(2) 16(3/4) days
(3) 16 days
(4) 15(3/4) days
(5) None of these

9. If 12 boys or 15 girls can do a work in 48 days, in what time will 24 boys and 6 girls do twice the work ?
(1) 42 days
(2) 40 days
(3) 45 days
(4) 30 days
(5) None of these

10. Seven men, five women and eight children were given an assignment of distributing 2000 books to students in a school over a period of three days. All of then distributed books on the first day. On the second day two women and three children remained absent and on the third day three men and
five children remained absent. If the ratio of the number of books distributed in a day by a man, a woman and a child was 5 : 4 : 2 respective, a total of approximately how many books were distributed on the second day ?
(1) 1000
(2) 800
(3) 650
(4) 900
(5) Cannot be determined


Answers :-
1. (2) 
2. (2)
3. (3) 
4. (5)
5. (5) 
6. (1)
7. (3)
8. (5)
9. (4)
10. (3)

Time And Work Previous Years Questions -I

1. 12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 days, how many women would be required ?
(1) 70            (2) 28          (3) 66            (4) 40          (5) None of these

2. 9 children can complete a piece of work in 360 days. 18 men can complete the same piece of work in 72 days and 12 women can complete the piece of work in 162 days. In how many days can 4 men, 12 women and 10 children together complete the piece of work ?
(1) 124         (2) 81          (3) 68             (4) 96           (5) None of these

3.Fifty six men can complete a piece of work in 24 days. In how many days can 42 men complete the same piece of work ?
(1) 18           (2) 32           (3) 98            (4) 48            (5) None of these

4. 42 women can do a piece of work in 18 days. How many women would be required do the same work in 21 days ?
(1) 36           (2) 24            (3) 30            (4) 44            (5) None of these

5. 30 men can do a piece of work in 16 days. How many men would be required to do the same work in 20 days ?
(1) 12          (2) 36            (3) 48            (4) 24             (5) None of these

6. 8 men can complete a piece of work in 4 days. 12 women can complete the same piece of work in 4 days whereas 8 children can complete the same piece of work in 8 days. 2 men, 8 children and 3 women work together for 2 days. If only women were to finish the remaining work in 2 days, how
many total women would be required ?
(1) 12          (2) 18            (3) 24            (4) 20             (5) None of these

7. 18 children can do a piece of work in 12 days. How many children would be required to do the same work in 8 days ?
(1) 12          (2) 18           (3) 24            (4) 27               (5) None of these

8. 8 men and 4 women together can complete a piece of work in 6 days. Work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined, in how many more days will the work be completed ?
(1) 5 days     (2) 8 days    (3) 6 days    (4) 4 days            (5) 9 days

9. B and C together can complete a work in 8 days, A and B together can complete the same work in 12 days and A and C together can complete the same work in 16 days. In how many days can A, B and C together complete the same work ?
(1) 3(9/13)    (2) 7(5/13)      (3) 7(5/12)         (4) 3(5/12)         (5) None of these

10. 10 men can complete a piece of work in 8 days. 20 women can complete the same piece of work in 6 days. In how many days 16 men 18 women together can complete the same piece of work ?
(1) 2(5/7)       (2) 3(6/7)        (3) 3(3/7)            (4) 2(3/7)            (5) None of these

11. Ayesha can complete a piece of work in 16 days. Amita can complete the same piece of work in 8 days. If both of them work together in how many days can complete the same piece of work ?
(1) 6 days      (2) 4(2/5) days       (3) 5(1/3) days          (4) 12 days       (5) None of these

12. 6 men can complete a piece work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day how
many men would be required totally ?
(1) 36               (2) 24                  (3) 18                (4) Cannot be determined        (5) None of these

13. 3 men can complete a piece of work in 6 days. 5 women can complete the same work in 18 days. In how many days will 4 men and 10 women together complete the same work ?
(1) 3 days         (2) 5 days           (3) 2 days         (4) 4 days               (5) None of these

14. 8 men can complete a piece of work in 20 days. 8 women can complete the same work in 32 days. In how many days will 5 men and 8 women together complete the same work ?
(1) 16 days       (2) 12 days        (3) 14 days          (4) 10 days             (5) None of these

15. 2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total
men would be required ?
(1) 4                 (2) 8                  (3) 6            (4) Cannot be determined     (5)None of these

16. Vikas gets Rs 350 for every day that he works. If he earns Rs 9,800 in a month of 31 days, for how many days did he work ?
(1) 25 days     (2) 30 days            (3) 24 days              (4) 28 days            (5) None of these

17. A water tank has three taps A, B and C. Tap A, when opened, can fill the water tank alone in 4 hours. Tap B, when opened, can fill the water tank alone in 6 hours and tap C, when opened, can empty the water tank alone in 3 hours. If taps A, B and C are opened simultaneously how long will it take to fill the tank completely ?
(1) 10 hours        (2) 8 hours        (3) 18 hours        (4) 12 hours            (5) None of these

18. 4 girls can do a piece of work in 8 days, 3 boys can do the same piece of work in 9 days, 7 men do the same piece of work in 2 days and 5 women can do the same piece of work in 4 days. Who is least efficient ?
(1) Boys            (2) Girls             (3) Women           (4) Men            (5) Boys and Men both

19. Two men alone or three women alone can complete a piece of work in 4 days. In how many days can 1 woman and one man together complete the same piece of work ?
(1) 6 days          (2) 24/5 days        (3) 12/ 1.75 days     (4) Cannot be determined  (5) None of these

20. Four examiners can examine a certain number of answer papers in 10 days by working for 5 hours a day. For how many hours in a day would 2 examiners have to work in order to examine twice the number of answer papers in 20 days ?
(1) 8 hours         (2) 7(1/2) hours       (3) 10 hours        (4) 8(1/2)hours           (5) None of these

21. 6 women and 6 men together can complete a piece of work in 6 days. In how many days can 15 men alone complete the piece of work if 9 women alone can complete the work in 10 days ?
(1) 6                (2) 5                       (3) 7.2               (4) Cannot be determined  (5) None of these

22. A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C
when completing the same task alone ?
(1) 2 : 5            (2) 2 : 7                (3) 3 : 7              (4) 1 : 5                   (5) 3 : 5


Answers :)
1. (1)
2. (2)
3. (2)
4. (1)
5. (4)
6. (1)
7. (4)
8. (1)
9. (2)
10. (5)
11. (3)
12. (1)
13. (1)
14. (1)
15. (2)
16. (4)
17. (4)
18. (2)
19. (2)
20. (3)
21. (5)
22. (4)

Data Interpretation For SBI mains

Directions for Questions 101-105: The following graph gives the data on the number of units of iPhones sold and price of an iPhone in various years. Answer the questions based on the line graph.

Question 101

In 2012 one-fourth of the number of iphones were sold at a price 10% more than the MRP, however to boost the sales 30% discount was given on the increased price and rest (three-fourth) of the units were sold in 2012 at this discounted price. What is the difference in revenue had all the iphones had been sold at the MRP in 2012?

Rs. 9765420 Rs. 9581600 Rs. 9864500 Rs. 9936500 None of these Question 102 In which year there was highest percentage increase in the number of iphones sold? 2013 2011 2010 2014 2012 Question 103 X% and Y% discount was allowed on the MRP of an iphone in 2011 and 2013 respectively, the number of units sold were as given in the graph, and the revenue from sale of iphones in 2011 and 2013 was Rs. 29656000 and Rs. 102765000 respectively, then what is the ratio of X and Y? 4:3 3:4 1:1 2:3 3:2 Question 104 What was the revenue from sale of iphones (assuming all iphones sold on MRP) in the year in which there was the highest increase in absolute terms in the sale of number of iphones? Rs. 1809 lakh Rs. 1209 lakh Rs. 649.6 lakh Rs. 370.7 lakh None of these Question 105 What is the average price of an iphone from 2009 to 2012? Rs. 52000 Rs. 57000 Rs. 48000 Rs. 55000 None of these

Quiz On CI and SI

1. Raviraj Invested an amount of Rs.10000 at a compound interest rate of 10% per annum for a period of three years.How much amount will raviraj get after 3 years.?

(a)    12340

(b)   13210

(c)    13320

(d)   13310

(e)   None of these

2. If the CI on a certain sum for 2 years at 3% be Rs 101.50, what would be the SI?

3. The Compound Interest on a certain sum for 2 years is Rs. 40.80 and simple interest is Rs 40.

Find the rate of interest per annum and the sum.

4.If the difference between CI and SI on a certain sum of money for 3 years at 6% pa is Rs.11016, 

find the sum.

(a)    3060000

(b)   1000000

(c)    5100000

(d)   1210000

(e)   None of these

5. The CI on a certain sum is Rs.104 for 2 years and SI is Rs 100. What is the rate percent?

(a)    2%

(b)   4%

(c)    8%

(d)   16%

(e)   None of these

6. Rs. 4800 becomes Rs.6000 in 4 years at a certain rate of compound interest. What will be the sum after 

12 years?

7. A man Deposits Rs. 1350 in a bank at 5% per annum and Rs 1150 in another bank at 6% per 

annum. Find the rate of Interest for the whole sum.

(a)    5.40%

(b)   6.40%

(c)    5.46%

(d)   11.5%

(e)  None of These

8.Out of a certain sum, 1/3rd is invested at 3%, 1/6th at 6% and the rest at 8%. If the simple interest 

for 2 years from all these investements amounts to Rs. 600, find the original sum.

(a)    Rs. 5000

(b)   Rs. 6000

(c)    Rs. 5200

(d)   Rs. 5500

(e)   None of these

10. What annual payment will discharge a debt of Rs. 770 in 5 years, the rate of interest being 5% per annum?

(a)    120

(b)   130

(c)    140

(d)   114

(e)  None of these

11. The rate of interest for the first 2 years is 3% per annum, for the next 3 years is 8% per annum and for the period beyond 5 years 10% per annum. If a man gets Rs 1520 as a simple interest for 6 years, how much did he deposited?

(a)    3800

(b)   4200

(c)    3000

(d)   Cant be determined

(e)   None of these

Normal time to be taken to solve these should be max. 9-11 minutes :)

Answers will be posted soon :))