11.
7 is added to a certain number; the sum is multiplied by 5; the product is divided by 9 and 3 is subtracted from the quotient. The remainder left is 12. The number is:
• A.
20
• C.
40
• B.
30
• D.
60
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Explanation :

Let the number be x. Then,

 5(x + 7) 9
- 3 = 12

5 (x + 7) - 27 = 108

5x + 35 = 135

5x = 100

x = 20

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12.
A class starts at 10 a.m. and lasts till 1.27 p.m. Four periods are held during this interval. After every period, 5 minutes are given free to the students. The exact duration of each period is:
• A.
42 minutes
• C.
51 minutes
• B.
48 minutes
• D.
53 minutes
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Explanation :

Time between 10 a.m. and 13.27 hours = 3 hrs. 27 min. = 207 min.

For three periods in between free time = 15 min.

Remaining time = (207 – 15) min. = 192 min.

Duration of each of the 4 periods =
 192 4
min. = 48 min.

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13.
The fluid contained in a bucket can fill four large bottles or seven small bottles. A full large bottle is used to fill an empty small bottle. What fraction of the fluid is left over in the large bottle when the small one is full?
•  A. 2 7
•  C. 4 7
•  B. 3 7
•  D. 5 7
• Report
Explanation :

Let the capacity of the bucket be x litres. Then,

Capacity of 1 large bottle =
 x 4
; Capacity of 1 small bottle =
 x 7

Fluid left in large bottle =
 x 4
-
 x 7
=
 3x 28

Required fraction =
 3x/28 x/4
=
 3x 28
-
 4 x
=
 3 7

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14.

 785 x 785 x 785 + 435 x 435 x 435 785 x 785 + 435 x 435 - 785 x 435
Simplifies to :
• A.
350
• C.
1220
• B.
785
• D.
1320
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Explanation :

Given exp. =
 a3 + b3 a2 + b2 - ab
= (a + b), where a = 785, b = 435

 = (785 + 435) = 1220.

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15.
Vidushi and Sanya distribute Rs. 100 each in charity. Vidushi distributes money to 5 more people than Sanya and Sanya gives each Re. 1 more than Vidushi. How many people are recipients of the charity?
• A.
45
• C.
90
• B.
60
• D.
None of these
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Explanation :

Suppose, Sanya and Vidushi donate money to x and (x + 5) people respectively.

Then,
 100 x
-
 100 x + 5
= 1

100 (x + 5) - 100x = x(x + 5)

x2 + 5x - 500 = 0

(x - 20) (x + 25) = 0

x = 20

Total number of recipients of charity = x + (x + 5) = 2x + 5 = 45

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