**Directions(1-10):** The following questions consists of two statements,you have to decide whether the data provided in the statements are sufficient to answer.

- Nik invested certain amount of money in a scheme offering 10% compound interest compounded annually. Kim invested Rs.1000 more than Nik in another scheme offering 9% simple interest. Find the amount invested by Nik.

**Statement I:**Difference in the interests earned by Nik and Kim after two years is Rs.90

**Statement II:**Difference in the interests earned by Nik and Kim after three years is Rs.279.II alone is sufficient.Both together necessary.I alone is sufficient.Either I or II.Both are not sufficient.Option A

Let the amount invested by Nik and Kim be Rs. x and Rs.(x+1000) resp.

From I: Interest earned by Nik after two years = x*{(1+0.10)^2 – 1} = Rs.0.21x

Interest earned by Kim after two years = (x+1000)*0.09*2 = Rs.0.18x+180

Either == 0.21x â€“ 0.18x â€“ 180 = 90

=>x = 9000

Or == 0.18x + 180 â€“ 0.21x = 90

=>x = 3000

value of x cannot be determined exactly.

Statement II: Interest earned by Nik after three years = x * {(1+0.10)^3 -1} = Rs.0.331x

Interest earned by Kim after three years = (x+1000)*0.09*3 = Rs.0.27x+270

Here ,0.061x = 549

=> x = 9000

II alone is sufficient. - A shopkeeper bought an article and sold it. What is the cost of the article?

**Statement I:**Profit earned by the shopkeeper is Rs.250 and selling price of the article is 30% less than the marked price of the article.

**Statement II:**Marked price of the article is 25% above the selling price. Shopkeeper marked the price of article Rs.2000 and profit percent earned is 60%.I alone is sufficient.Either I or II.Both are not sufficient.II alone is sufficient.Both together necessary.Option D

From I: Let the MP be Rs.x

SP = 70% of x = Rs.7x/10 Profit = Rs.250

Let CP be Rs.y.

So, y + 250 = 7x/10

I alone is not sufficient.

From II: Let SP be Rs.x

P = (2000/125)*100 = Rs.1600

CP = (1600*100)/160 = Rs.1000

II alone is sufficient. - After 3 years, ratio of age of P and Q will become 17:15. Find the difference between the age of P and Q.

**Statement I:**3 years ago, the ratio of the age of P and age of Q was 7:6.

**Statement II:**The ratio of age P after 5 years and age of Q 7 years ago is 9:5.Both together necessary.II alone is sufficient.Either I or II.Both are not sufficient.I alone is sufficient.Option C

Let the present age of P and Q be x and y years.

So,(x+3)/(y+3) = 17/15 =>x = (6+17y)/15

From I: (x-3)/(y-3)= 7/6

=>y = 27

Then x = 31

Required Difference = 31 â€“ 27 = 4 years

I alone is sufficient.

From II: (x+5)/(y-7) = 9/5

=>y = 27

x = 31

Required Difference = 31 â€“ 27 = 4 years

II alone is sufficient.

Either I or II. - If an item is sold at 25% discount. Then it gives a profit of 25%. Find the selling price of the item.

**Statement I:**If it is sold for Rs.45 more, then the profit percentage is 40%.

**Statement II:**If the marked price of the item is increased by 10% and discount rate remains the same, then the profit percentage is 37.5%.Either I or II.Both are not sufficient.II alone is sufficient.I alone is sufficient.Both together necessary.Option D

Let CP be Rs.x

SP = Rs.1.25x

MP = 1.25x/0.75 = Rs.(5/3)x

From I: (1.25x + 45) = 1.4x

=> x = Rs.300

I alone is sufficient.

From II: New MP = (5/3)x*1.1 = Rs.(5.5/3)x

Now, (5.5/3)x *0.75 =1.375x

II is not sufficient. - Four persons A,B, C and D are hired to do a work. A,C and D can complete the task in 16 days while working together. Find the number of days taken by B alone to complete the task.

**Statement I:**C and D can complete the work in 24 days. B is 100% more efficient than A.

**Statement II:**A alone can complete the work in 48 days, and ratio of efficiency of C and D is 1:2 resp.Both together necessary.I alone is sufficient.Both are not sufficient.Either I or II.II alone is sufficient.Option B

From I: Let the total work LCM(16,24) = 48 units

Number of units of work done by A,C and D in one day = 48/16 = 3 units

Number of units of work done by C and D in one day = 48/24 = 2 units

Number of days taken by A to complete the work in one day = 3-2 = 1 units

Therefore, number of days taken by A to complete the work = 48/1 = 48 days

So, time taken by B to complete the work = 48/2 = 24 days

I alone is sufficient.

From II: Let the efficiency of C and D be x and 2x resp.

1/48 + x + 2x = 1/16

=> x = 1/72

II alone is not sufficient. - Find the marks obtained by Simran in half-yearly exam, if the sum of marks obtained by Simran and Raj in half-yearly exam is 1410.

**Statement I:**The ratio of marks obtained by Simran and Raj in quarterly exam was 9:8 resp.

**Statement II:**The ratio of marks obtained by Simran in quarterly exam to the half-yearly exam is 2:3 resp. while ratio of marks by Raj in quarterly exam to the half-yearly exam is 4:5 resp.I alone is sufficient.Both together necessary.Both are not sufficient.Either I or II.II alone is sufficient.Option B

From I: Let the marks obtained by Simran and Raj in quarterly exam be 9x and 8x resp.

This alone is not sufficient.

From II: Let the marks obtained by Simran in quarterly and half-yearly exam be 2y and 3y resp.

Let the marks obtained by Raj in quarterly and half-yearly exam by 4z and 5z resp.

This alone is not sufficient.

Combining these two equations,we get 9x*3/2 + 8x*5/4 = 1410

=> x = 60

Marks obtained by Simran in half-yearly exam = 9x*3/2 = 810

Both together necessary. - A bag contains a total of (x+6) balls of three colors like White,Black and Brown such that the ratio of number of White and Brown balls is 3:4 resp. and the probability of drawing a Black ball is 1/3. Find the number of balls in the bag.

**Statement I:**Probability of drawing a white ball is 2/7.

**Statemnet II:**The number of black balls in the bag is 2 less than the number of brown balls .Either I or II.I alone is sufficient.II alone is sufficient.Both are not sufficient.Both together necessary.Option C

Let the number of White and Brown color balls be 3x and 4x resp.

So, the number of Black balls = (y+6)- (3x+4x) = (y â€“ 7x +6)

Probability of drawing the Black ball = 1/3 (y â€“ 7x + 6)/(y+6) = 1/3

=>21x = 2y + 12 —-(1)

From I: Probability of drawing the White ball = 2/7

3x/(y+6) = 2/7

21x = (2y+12) —-(2)

Both the equations are same, so this canâ€™t be solved using Statement I.

From II: (y â€“ 7x + 6) = 4x â€“ 2

=> y = 11x â€“ 8 —-(3)

From equations (1) and (2), we get

21x â€“ 12 = 22x â€“ 16

=> x = 4

So, y = 11*4 â€“ 8 = 36

Total number of balls in the bag = 36+6 = 42

II is alone sufficient. - Find the time taken by 3 males and 5 females to plough the field while working together.

**Statement I:**1 male can plough half of the field in 12 days, 2 females can plough two fields of the same area and same type in 20 days.

**Statement II:**2 males can plough a field in 12 days and 2 females can plough the same field in 10 days.Both are not sufficient.I alone is sufficient.Either I or II.Both together necessary.II alone is sufficient.Option C

From I: Time taken by 3 male t plough the field = 12/(3/2) = 8 days

Time taken by 5 female to plough the field = (20*2)/(5*2 ) = 4 days

So, the time taken by 3 male and 5 female to plough the field while working together

= (8*4)/(8+4) = (8/3) days

I alone is sufficient.

From II: Time taken by 3 male t plough the field = 12/(3/2) = 8 days

Time taken by 5 female to plough the field = (10*2)/(5 ) = 4 days

So, the time taken by 3 male and 5 female to plough the field while working together = (8*4)/(8+4)

= (8/3) days

Either I or II. - A container contains â€˜xâ€™ litres of a mixture of water and alcohol in the ratio 7:22 resp. A man takes out â€˜yâ€™ litres of the mixture from the container and then mixes 28 litres of a mixture of water and alcohol in the ratio of 6:1 resp. in that container.

Find the value of x.

**Statement I:**The ratio of water and alcohol becomes 3:8 resp. after mixing 28 litres of a mixture of water and alcohol in the ratio of 6:1 resp.

**Statement II:**The amount of water in the container becomes 150 litres after mixing 28 litres of a mixture of water and alcohol in the ratio 6:1 resp.Both together necessary.Both are not sufficient.II alone is sufficient.Either I or II.I alone is sufficient.Option B

Initially amount of water and alcohol be 7x and 22x resp. Amount of water and alcohol taken out be 7y and 22y resp.

Statement I: (7x â€“ 7y + 24)/(22x â€“ 22y + 4) = 3/8

=>x â€“ y = 18

I alone is not sufficient.

From II: 7x â€“ 7y + 24 = 150

=> x â€“y = 18

II alone is not sufficient.

Combining both the equations, we get

(7x â€“ 7y + 24)/(22x â€“ 22y + 4 ) = 3/8

=>x â€“ y = 18

And 7x â€“ 7y + 24 = 150

=>x â€“ y = 18

Both are not sufficient. - A bag contains red,blue and green balls in the ratio of 4:5:3 resp. Find the total number of balls in the bag.

**Statement I:**Probability of drawing two blue balls from the bag is 1/6.

**Statement II:**Probability of drawing a green ball from the bag is Â¼.Either I or II.Both are not sufficient.I alone is sufficient.II alone is sufficient.Both together necessary.Option C

From I: Probability of choosing two blue ball from the bag = 5xC2/12xC2 = 1/6

=>x = 3

Total number of balls = 12*3 = 36

I alone is sufficient.

From II: Probability of drawing a green ball = 3xC1/12xC1 = Â¼

=> Â¼ = Â¼

II is not sufficient.