The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

A.

1

B.

2

C.

3

D.

4

Answer: Option B

Explanation:

Let the numbers 13a and 13b.

Then, 13a x 13b = 2028

ab = 12.

Now, the co-primes with product 12 are (1, 12) and (3, 4).

[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]

So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).

Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?

A.

Rs. 17,000

B.

Rs. 20,000

C.

Rs. 25,500

D.

Rs. 38,000

Answer: Option D

Explanation:

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.

Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:

A.

1

3

B.

2

3

C.

2

5

D.

3

5

Answer: Option B

Explanation:

By the rule of alligation, we have:

Strength of first jarStrength of 2^{nd} jar

40%

Mean Strength
26%

19%

7

14

So, ratio of 1^{st} and 2^{nd} quantities = 7 : 14 = 1 : 2

Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

A.

57

B.

67

C.

77

D.

87

Answer: Option C

Explanation:

Money collected = (59.29 x 100) paise = 5929 paise.

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m^{3}) is:

A.

4830

B.

5120

C.

6420

D.

8960

Answer: Option B

Explanation:

Clearly, l = (48 - 16)m = 32 m,

b = (36 -16)m = 20 m,

h = 8 m.

Volume of the box = (32 x 20 x 8) m^{3} = 5120 m^{3}.