## Sunday, 23 October 2016

### Set A

1.One angle of a regular polygon measures 177°How many sides does it have?
(a) 89
(b) 120
(c) 177
(d) 183

2.One angle of a parallelogram measures (2x + y)°Another angle of the same quadrilateral but not the opposite angle) measures (x + 2y)° . What is (x + y) ?
(a) 30
(b) 60
(c) 90
(d) 120

3.A right triangle with legs measuring 12 cm and 16 cm is inscribed in a circle. What is the circumference of the circle in centimeters?
(a)14π
(b) 16π
(c) 20π
(d) 28π

4.A square has a diagonal measuring 8 cm. When its area is expressed as 2K square centimeters,what is K?
(a) 4
(b) 5
(c) 6
(d) 7

5.When the base of a triangle is increased by 10% and he altitude to this base is decreased by 10%,the area is
(a) increased by 10%
(b) decreased by 10%
(c) increased by 1%
(d) decreased by 1%

6.In the figure given below, triangle ABC is right-angled. What is the area of
triangle ABD?

(a) 6
(b) 7
(c) 8
(d) 9

7.In triangle ABC, ∠A is equal to 120°. A point D is inside
the triangle such that ∠DBC = 2∠ABD and ∠DCB =
2∠ACD. What is the measure of ∠BDC?

(a) 135
(b) 140
(c) 145
(d) 150

8.The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field ?
(a). 18 meter
(b). 20 meter
(c). 22 meter
(d). 25 meter

9.A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required ?
(a) 88 feet
(b)86 feet
(c)84 feet
(d)82 feet

10.The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. What is the length of the rectangle?
(a).18 cm
(b).16 cm
(c).40 cm
(d).20 cm

solution
1.Each angle of a regular polygon =(n- 2)180°/n= 117°
n = 120

2.Sum of two consecutive angles of a Πgm is 180o.
Hence 2x+y+x+2y = 180° ⇒ x + y = 60°

3.

BC = √12^2  +16^2= 400=20cm
∴radius of circle = 10cm (∴angle in a semi circle is 90o)
∴circumference = 2λ.10 = 20λcm

4.Diagonal of a sq with side a = a √2
∴a √2 = 8  ⇒ a =8/√2= 4√2
Hence area =(4√ 2)^2 = 32= 2^5 = Hence K =5.

5.The new area= 1/2×1.1×base × 0.9× height = original area × 0.99. Therefore the area decreases by 1.1.

6.Area of the triangle ABD= 1/2×base× height= 1/2×3×6= 9 units.

7.From the given figure

3∝ + 3β + A= 180o ∝ + β= 20o
∠BDC= 180o – 2 (∝ + β)= 140o
Then length =(115y/100)metres.
Area = y x115y/100 = 460
=>y^2=(460x100/115)
=>y^2=400
y=20
So breath is 20 m

9.We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 20 * Breadth = 680
Area to be fenced = 2B + L = 2*34 + 20
= 88 feet

Then length = 2x cm
Area = lb = x × 2x = 2x^2
New length = (2x - 5)
New breadth = (x + 5)
New Area = lb = (2x - 5)(x + 5)
But given that new area = initial area + 75 sq.cm.
=> (2x - 5)(x + 5) = 2x^2 + 75
=> 2x^2 + 10x - 5x - 25 = 2x^2 + 75
=> 5x - 25 = 75
=> 5x = 75 + 25 = 100
=> x = 100/5 = 20 cm
Length = 2x = 2 × 20 = 40cm

### Set B

1.A man sold an item for RS 135,00 at a loss of 25%. What will be the selling price of same item if he sells it at a profit of 25% ?
(a)RS 22700
(b)RS 23500
(c)RS 22500
(d)RS 22440

2.The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The smallest angle of a triangle is one-fourth the largest angle of the quadrilateral. Largest angle of the triangle is 10° more than second largest angle of the triangle. What is the second largest angle of the triangle?
(a).80°
(b).60°
(c).70°
(d).80
3.The difference between the compound intrest and simple intrest on an amount of Rs.46000 for 2 year is Rs.73.6. what the rate of intrest?
(a).4.25
(b).4
(c).5
(d).3.75

4.The profit earned by a company is to be distributed among the managers and officers in the ratio of 7:5. If the number of managers and officers is in the ratio of 7:12 the amount received by each officers is 30,000 what was the total profit earned if the number of managers was28?
(a). 35 lakh
(b). 17.5 lakh
(c). 34.56 lakh
(d). 19 lakh

5.The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number?
(a). 60
(b). 80
(c). 40
(d). 120

6.A man can row 4 kmph is still water. If the river is running at 2 kmph it takes 90 min to row to a place and back. How far is the place?
(a). 2 km
(b). 4 km
(c). 5 km
(d). 2.25 km

7. man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?
(a). 3 km
(b). 4 km
(c). 5 km
(d). 6 km

8.What day of the week will 22 Apr 2222 be?
(a). Monday
(b). Tuesday
(c). Sunday
(d). Thursday

9.A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew ¼ of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs. 760. What is A's share in the profit?
(a). 310
(b). 330
(c). 370
(d). 350

10.A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 31 per kg, then his gain percent is
(a).65.33%
(b).66.13%
(c).68.14%
(d).70.15%

1.(c)
C.P. of the item = ( 13500 ×100 )/75 = Rs 18000
So, Reqd. S.P. of the item = (18000 × 125)/100=Rs 22500

2.(c)
The largest angle of the quadrilateral (6 ×360)/(6+4+3+5) = 120 degrees
Smallest angle of the triangle = 120 × 1/4 = 30 degrees
If second largest angle of the triangle = (x + 10)
So 30+ x+ x+10 = 180 , x = 70 degrees

3(b)
sum = diffx(100/r)^2
or,46000 = (736x10000)/r^2
or,r^2 = 736/46 = 16
r = 4

4(c)Let the managers get y Rs.
7/12 x y/30000 = 7/5
y = 72000
Total money = 72000X28x12/7= 34.56 lakh

5(b)
Let the original number be x.
Let A be the value obtained when x is increased by 12.5%.
Therefore, A = x + 12.5% of x
Let B be the value obtained when x is decreased by 25%.
Therefore, B = x - 25% of x
The question states that A - B = 30
i.e., x + 12.5% of x - (x - 25% of x) = 30
x + 12.5% of x - x + 25% of x = 30
37.5% of x = 30
x = 30/37.5*100 = 80

6(d)
Speed in still water = 4 kmph
Speed of the stream = 2 kmph
Speed upstream = (4-2)= 2 kmph
Speed downstream = (4+2)= 6 kmph
Total time = 90 minutes = 90⁄60 hour = 3⁄2 hour
Let L be the distance. Then
L/6+L/2=32
=> L + 3L = 9
=> 4L = 9
=> L = 9⁄4= 2.25 km

7(d)
Explanation :
If a car covers a certain distance at x kmph and an equal distance at y kmph,
the average speed of the whole journey = 2xy/(x+y) kmph
Hence, average speed = (2×3×2)/(2+3) =12/5 km/hr
Total time taken = 5 hours
=Distance travelled =12/5×5=12 km
=Distance between his house and office =12/2=6 km

8(a)
Explanation :
22 Apr 2222 = (2221 years + period from 1-Jan-2222 to 22-Apr-2222)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2200
= Number of odd days in 200 years
= 5 x 2 = 10 = 3
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 2201-2221
= 16 normal years + 5 leap years
= 16 x 1 + 5 x 2 = 16 + 10 = 26 = 5 odd days
Number of days from 1-Jan-2222 to 22 Apr 2222
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 22(Apr) = 112
112 days = 0 odd day
Total number of odd days = (0 + 3 + 5 + 0) = 8 = 1 odd day
1 odd days = Monday
Hence 22 Apr 2222 is Monday.

9(B)
Explanation :
Ratio of the initial capital of A and B = 4 : 5
Hence we can take the initial capitals of A and B as 4x and 5x respective
Ratio in which profit will be divided
= (4x*3) + (3/4)*(4x)*7 : (5x*3)+ (4/5)*(5x)*7
= 12+21 : 15+28
= 33 : 43
A's share = 760 * 33/76 = 330

10(a)
Explanation:
Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 31) = Rs. 248.
Profit = 248 -150 = 98
So, Profit % = (98/150) * 100 = 65.33%

### Set C

1. The sum of the circumference of a circle and the perimeter of a rectangle is 132 cm. The area of the rectangle is 112 sq cm and breadth of the rectangle is 8 cm. What is the area of the circle ?
(a) 616 sq cm
(b) 540 sq cm
(c) 396 sq cm
(d) Cannot be determined

2. The cost of 5 kg of apple is equal to the cost of 12 kg of rice. The cost of 3 kg of flour is equal to one kg of rice. The cost of one kg. of flour is RS 17.50. What is the total cost of 3 kg of apple, 2 kg of rice and 4 kg of flour together ?
(a) RS 543
(b) RS 527
(c) RS 563
(d) RS 553

3. Thirty-five per cent of 740 is 34 more than a number. What is two-fifth of the number ?
(a) 45
(b) 90
(c) 180
(d) 120

4. The ratio between the angles of a quadrilateral is 6 : 3 : 4 : 5. The smallest angle of a triangle is one-fourth the largest angle of the quadrilateral. Largest angle of the triangle is 10° more than second largest angle of the triangle. What is the second largest angle of the triangle ?
(a) 80°
(b) 60°
(c) 70°
(d) Cannot be determined

5. A train covered a distance of 1235 km in 19 hours. Also, the average speed of a car is four-fifth the average speed of the train. How much distance will the car cover in 22 hours ?
(a) 1234 km
(b) 1144 km
(c) 1134 km
(d) 1244 km

6. A certain amount was to be distributed among A, B and C in the ratio 1 : 2 : 3 respectively, but was erroneously distributed in the ratio 4 : 3 : 2 respectively. As a result of this, C got Rs. 60 less. What is the total amount?
(a) Rs. 216
(b) Rs. 48
(c) Rs. 108
(d) Rs. 36

7. Prashant scored 83 marks in subject A. He scored 75% marks in subject B and X marks in subject C. Maximum marks in each subject were 120. The overall percentage marks obtained by prashant in all three subjects together were 80%. How many marks did he score in subject C?
(a) 94
(b) 106
(c) 85
(d) 115

8. Monika enters a shop to buy pen, pencils and erasers. She has to buy at least 7 units of each. She buys more pencils than pen and more erasers than pencils. She picks up a total of 26 items. How many pencils does she buy?
(a) 10 or 11
(b) 9 or 10
(c) 8 or 9
(d) 7 or 9

9. Rs. 31,394 are divided between A and B in the ratio 5 : 6. What is the difference between thrice the share of A and twice the share of B?
(a) Rs. 6582
(b) Rs. 5862
(c) Rs. 8562
(d) Rs. 8652

10. Sum of three consecutive numbers is 2475. What is 35% of the smallest number?
(a) 251.6
(b) 288.4
(c) 308.4
(d) 296.8

1. (a):
Length of the rectangle = 112/8 = 14 cm, so  perimeter= 44 cm,
Circumference= 132-44=88 cm,
R = (88 × 7 )/(2 ×22)  = 14cm
So area = 616cm

2. (d):

3. (b):
Number = 740 × 35/100 - 34 = 225
2/5  of the number=90

4. (c):
The largest angle of the quadrilateral (6 ×360)/(6+4+3+5) = 120 degrees
Smallest angle of the triangle = 120 × 1/4 = 30 degrees
If second largest angle of the triangle = (x + 10)
So 30+ x+ x+10 = 180 , x = 70 degrees

5. (b):
6. (a)
Let the total amount be x.
C’s original share = 3x / 6 = x / 2
C’s new share = 2x / 9
Now
(x / 2) – (2x / 9) = 60
x = 216

7. (d)
prashant marks in A = 83
prashant marks in B = 75% of 120 = 90
Now
(83 + 90 + x) / 360 * 100 = 80
x = 115

8. (c)
No. of erasers > No of pencils > No of pens
Possible combinations
Erasers = 11, Pencils = 8, Pens = 7
OR
Erasers = 10, Pencils = 9, Pens = 7

9. (c)
Let the shares of A and B be 5x and 6x. Now
5x + 6x = 31394
x = 2854
Required difference = (3 * 5)x – (2 * 6)x = 3x = 8562

10. (b)
Let the numbers be x, x + 1 and x + 2. Now
x + (x + 1) + (x + 2) = 2475
x = 824
Required number = 35% of 824 = 288.4