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Instruction:

Total number of questions : 20 .

Time alloted : 30 minutes.

Each question carry 1 mark, no negative marks.

1.
A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:

Answer: Option C

Explanation:

By the rule of alligation, we have:

Profit on 1^{st} part
Profit on 2^{nd} part
8%
Mean Profit
14%
18%
4
6

Ration of 1^{st} and 2^{nd} parts = 4 : 6 = 2 : 3

Quantity of 2^{nd} kind =
3
x 1000
kg
= 600 kg.
5

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2.
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

Answer: Option C

Explanation:

By the rule of alligation:

Cost of 1 kg pulses of 1^{st} kind
Cost of 1 kg pulses of 2^{nd} kind
Rs. 15
Mean Price
Rs. 16.50
Rs. 20
3.50
1.50

Required rate = 3.50 : 1.50 = 7 : 3.

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3.
The certain worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. The banker's gain is:

Answer: Option C

Explanation:

B.G. =
(T.D.)^{2}
= Rs.
160 x 160
= Rs. 16.
P.W.
1600

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4.
The banker's gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:

Answer: Option D

Explanation:

T.D. =
B.G. x 100
= Rs.
6 x 100
= Rs. 50.
R x T
12 x 1

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Direction (for Q.No. 5): Find the odd man out.

5.
835, 734, 642, 751, 853, 981, 532

Answer: Option A

Explanation:

In each number except 751, the difference of third and first digit is the middle one.

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6.
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

Answer: Option A

Explanation:

Formula for converting from km/hr to m/s:
X km/hr =
X x
5
m/s.
18

Therefore, Speed =
45 x
5
m/sec
=
25
m/sec.
18
2

Total distance to be covered = (360 + 140) m = 500 m.

Required time =
500 x 2
sec
= 40 sec.
25

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7.
If m and n are whole numbers such that m ^{n} = 121, the value of (m - 1)^{n + 1} is:

Answer: Option D

Explanation:

We know that 11^{2} = 121.

Putting m = 11 and n = 2, we get:

(m - 1)^{n + 1} = (11 - 1)^{(2 + 1)} = 10^{3} = 1000.

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8.
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

Answer: Option C

Explanation:

In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.

Thus, we have MTHMTCS (AEAI).

Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

Number of ways of arranging these letters =
8!
= 10080.
(2!)(2!)

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters =
4!
= 12.
2!

Required number of words = (10080 x 12) = 120960.

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9.
Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

Answer: Option B

Explanation:

(20 x 16) women can complete the work in 1 day.

1 woman's 1 day's work =
1
.
320

(16 x 15) men can complete the work in 1 day.

1 man's 1 day's work =
1
240

So, required ratio
= 4 : 3 (cross multiplied)

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10.
Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

Answer: Option B

Explanation:

Let B be turned off after x minutes. Then,

Part filled by (A + B) in x min. + Part filled by A in (30 -x ) min. = 1.

x
2
+
1
+ (30 - x ).
2
= 1
75
45
75

11x
+
(60 -2x )
= 1
225
75

11x + 180 - 6x = 225.

x = 9.

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Direction (for Q.No. 11):

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

11.

How many marks did Tarun secure in English?

I.

The average mark obtained by Tarun in four subjects including English is 60.

II.

The total marks obtained by him in English and Mathematics together are 170.

III.

The total marks obtained by him in Mathematics and Science together are 180.

Answer: Option E

Explanation:

I gives, total marks in 4 subjects = (60 x 4) = 240.

II gives, E + M = 170

III gives, M + S = 180.

Thus, none of (A), (B), (C), (D) is true.

Correct answer is (E).

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12.
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

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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13.
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:

14.
If one-third of one-fourth of a number is 15, then three-tenth of that number is:

Answer: Option D

Explanation:

Let the number be x .

Then,
1
of
1
of x = 15 x = 15 x 12 = 180.
3
4

So, required number =
3
x 180
= 54.
10

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15.
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

Answer: Option B

Explanation:

Let the ten's and unit digit be x and
8
respectively.
x

Then,
10x +
8
+ 18 = 10 x
8
+ x
x
x

10x ^{2} + 8 + 18x = 80 + x ^{2}

9x ^{2} + 18x - 72 = 0

x ^{2} + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = 2.

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Direction (for Q.Nos. 16 - 18): Find out the wrong number in the series.

16.
1, 3, 10, 21, 64, 129, 356, 777

Answer: Option E

Explanation:

A x 2 + 1, B x 3 + 1, C x 2 + 1, D x 3 + 1 and so on.

So, 356 is wrong.

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17.
196, 169, 144, 121, 100, 80, 64

Answer: Option E

Explanation:

Numbers must be (14)^{2} , (13)^{2} , (12)^{2} , (11)^{2} , (10)^{2} , (9)^{2} , (8)^{2} .

So, 80 is wrong.

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18.
40960, 10240, 2560, 640, 200, 40, 10

19.
The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:

Answer: Option A

Explanation:

Let AB be the tree and AC be its shadow.

Let ACB = .

Then,
AC
=
3 cot = 3
AB

= 30º.

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Direction (for Q.No. 20): Find out the wrong number in the given sequence of numbers.

20.
125, 127, 130, 135, 142, 153, 165

Answer: Option D

Explanation:

Prime numbers 2, 3, 5, 7, 11, 13 are to be added successively.

So, 165 is wrong.

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