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Instruction:

Total number of questions : 20.

Time alloted : 30 minutes.

Each question carry 1 mark, no negative marks.

In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:

86 sec

80 sec

76 sec

None of these

Answer: Option B

Explanation:

B runs 45 m in 6 sec.

2

B covers 300 m in 6 x 2 x 300 sec = 80 sec.

45

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

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).

Clearly, there are 2 such pairs.

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The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

101

107

111

185

Answer: Option C

Explanation:

Let the numbers be 37a and 37b.

Then, 37a x 37b = 4107

ab = 3.

Now, co-primes with product 3 are (1, 3).

So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).

Greater number = 111.

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In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

266

5040

11760

86400

None of these

Answer: Option C

Explanation:

Required number of ways

= (⁸C₅ x ¹⁰C₆)

= (⁸C₃ x ¹⁰C₄)

=	8 x 7 x 6	x	10 x 9 x 8 x 7
	3 x 2 x 1		4 x 3 x 2 x 1

= 11760.

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If a - b = 3 and a² + b² = 29, find the value of ab.

Answer: Option A

Explanation:

2ab = (a² + b²) - (a - b)²

= 29 - 9 = 20

ab = 10.

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If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

2 : 5

3 : 7

5 : 3

7 : 3

Answer: Option C

Explanation:

Let 40% of A = 2 B

3

Then, 40A = 2B

100 3

2A = 2B

5 3

A = 2 x 5 = 5

B 3 2 3

A : B = 5 : 3.

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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?

Rs. 17,000

Rs. 20,000

Rs. 25,500

Rs. 38,000

Answer: Option D

Explanation:

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

Then, 2x + 4000 = 40

3x + 4000 57

57(2x + 4000) = 40(3x + 4000)

6x = 68,000

3x = 34,000

Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.

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A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:

Rs. 12

Rs. 15

Rs. 18

Rs. 21

Answer: Option B

Explanation:

Dividend on Rs. 20 = Rs. 9 x 20 = Rs. 9 .

100 5

Rs. 12 is an income on Rs. 100.

Rs. 9 is an income on Rs. 100 x 9 = Rs. 15.

5 12 5

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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:

1	13	hours
	17

2	8	hours
	11

3	9	hours
	17

4	1	hours
	2

Answer: Option C

Explanation:

Net part filled in 1 hour 1 + 1 - 1 = 17 .

5 6 12 60

The tank will be full in 60 hours i.e., 3 9 hours.

17 17

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10.

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:

60 gallons

100 gallons

120 gallons

180 gallons

Answer: Option C

Explanation:

Work done by the waste pipe in 1 minute = 1 - 1 + 1

15 20 24

= 1 - 11

15 120

= - 1 . [-ve sign means emptying]

40

Volume of 1 part = 3 gallons.

40

Volume of whole = (3 x 40) gallons = 120 gallons.

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11.

A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?

Rs. 18.20

Rs. 70

Rs. 72

Rs. 88.25

Answer: Option C

Explanation:

C.P. = Rs. 100 x 392 = Rs. 1000 x 392 = Rs. 320

122.5 1225

Profit = Rs. (392 - 320) = Rs. 72.

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12.

If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is:

Rs. 768

Rs. 968

Rs. 1960

Rs. 2400

Answer: Option A

Explanation:

P.W. = 100 x T.D. = 100 x 168 = 600.

R x T 14 x 2

Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768.

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13.

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:

Answer: Option B

Explanation:

By the rule of alligation, we have:

Strength of first jar Strength of 2^nd jar
40% Mean
Strength
26% 19%
7 14

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

Required quantity replaced = 2

3

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14.

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:

39, 30

41, 32

42, 33

43, 34

Answer: Option C

Explanation:

Let their marks be (x + 9) and x.

Then, x + 9 = 56 (x + 9 + x)

100

25(x + 9) = 14(2x + 9)

3x = 99

x = 33

So, their marks are 42 and 33.

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15.

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:

Answer: Option C

Explanation:

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

Number of members = 5929 = 77.

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16.

How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?

None of these

Answer: Option B

Explanation:

Sum of decimal places = 7.

Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.

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17.

How many times do the hands of a clock coincide in a day?

Answer: Option C

Explanation:

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

The hands overlap about every 65 minutes, not every 60 minutes.

The hands coincide 22 times in a day.

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18.

At what time between 9 and 10 o'clock will the hands of a watch be together?

45 min. past 9

50 min. past 9

49	1	min. past 9
	11

48	2	min. past 9
	11

Answer: Option C

Explanation:

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.

55 min. spaces gained in 60 min.

45 min. spaces are gained in 60 x 45 min or 49 1 min.

55 11

The hands are together at 49 1 min. past 9.

11

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19.

How much does a watch lose per day, if its hands coincide every 64 minutes?

32	8	min.
	11

36	5	min.
	11

90 min.

96 min.

Answer: Option A

Explanation:

55 min. spaces are covered in 60 min.

60 min. spaces are covered in 60 x 60 min. = 65 5 min.

55 11

Loss in 64 min. = 65 5 - 64 = 16 min.

11 11

Loss in 24 hrs = 16 x 1 x 24 x 60 min. = 32 8 min.

11 64 11

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20.

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 m³) is:

4830

5120

6420

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) m³ = 5120 m³.

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