SSC CGL 2015: Quant Quiz

1.There is 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 14,000 after 3 years at the same rate?

A. Rs.3794

B. Rs.3714

C. Rs.4612

D. Rs.4634

2.The difference between simple interest and compound on Rs. 2400 for one year at 10% per annum reckoned half-yearly is:

A. Rs. 4

B. Rs. 6

C. Rs. 3

D. Rs. 2

3. A tree increases annually by 1⁄5 th of its height. If its height today is 50 cm, what will be the height after 2 years?

A. 64 cm

B. 72 cm

C. 66 cm

D. 84 cm

4.The sum of ages of 5 children born at the intervals of 3 years each is 50 years. Find out the age of the youngest child?

A. 6 years

B. 5 years

C. 4 years

D. 3 years

5.Ayisha's age is 1/6th of her father's age. Ayisha 's father's age will be twice the age of Shankar's age after 10 years. If Shankar's eight birthdays was celebrated two years before, then what is Ayisha 's present age.

A. 10 years

B. 12 years

C. 8 years

D. 5 years

6.My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age my father when my brother was born?

A. 35 years

B. 34 years

C. 33 years

D. 32 years

7. Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal.

A. 40 years

B. 38 years

C. 42 years

D. 36 years

8.A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet?

A. 126 sq. ft.

B. 64 sq. ft.

C. 100 sq. ft.

D. 102 sq. ft.

9.The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 800 per sq. metre.

A. Rs.12000

B. Rs.19500

C. Rs.18000

D. Rs.16500.

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

Answers:

1.D
Let P = Rs.100 

Simple Interest = Rs. 80 ( ∵ 80% increase is due to the simple interest)

Rate of interest=(100×SI)/PT=(100×80)/100×8=10% per annum

Now let's find out the compound interest of Rs. 14,000 after 3 years at 10%
P = Rs.14000
T = 3 years
R = 10%
Amount after 3 years =P(1+R/100)^T=14000(1+10/100)^3=14000(110/100)^3=14000(11/10)^3=14×11^3=18634
Compound Interest = Rs.18634 - Rs.14000 = Rs.4634

2.B

3.B
This problem is similar to the problems we saw in compound interest. 
We can use the formulas of compound interest here as well.
Rate of increase = 1/5×100=20%
Height after 2 years = P(1+R/100)^T=50(1+20/100)^2=50(1+1/5)^2=50(6/5)^2=(50×6×6)/(5×5)=2×6×6=72 cm

4.C

5.D
Consider Ayisha's present age = x
Then her father's age = 6x
Given that Ayisha 's father's age will be twice the age of Shankar's age after 10 years
Shankar's age after 10 years = ½(6x + 10) = 3x + 5
Also given that Shankar's eight birthdays was celebrated two years before 

Shankar's age after 10 years = 8 + 12 = 20
3x + 5 = 20
x = 15/3 = 5
Ayisha 's present age = 5 years

6.D
Let my age = x
Then
My brother's age = x + 3
My mother's age = x + 26
My sister's age = (x + 3) + 4 = x + 7
My Father's age = (x + 7) + 28 = x + 35
age my father when my brother was born = x + 35 – (x + 3) = 32

7.A
Let the age of the son before 8 years = x.
Then age of Kamal before 8 years ago = 4x
After 8 years, Kamal will be twice as old as his son 
4x + 16 = 2(x + 16)
 x = 8
Present age of Kamal = 4x + 8 = 4×8 +8 = 40

8.A
Let l = 9 ft.
Then l + 2b = 37
2b = 37 - l = 37 - 9 = 28
b = 28/2 = 14 ft.
Area = lb = 9 × 14 = 126 sq. ft.

9.D
Area = 5.5 × 3.75 sq. metre.
Cost for 1 sq. metre. = Rs. 800
Hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = Rs. 16500

10.C
Let breadth = x cm
Then length = 2x cm
Area = lb = x × 2x = 2x2 
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

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SSC 2015:Brief Notes on Average With Quiz

TIPS FOR SOLVING QUESTIONS RELATED TO AVERAGE:

1. The average of a number of quantities of the same kind is equal to their sum divided by the number of those quantities. Thus,

Average =  Sum of the quantities / Number of quantities

Also, Sum of the quantities = Average x Number of quantities.

2. If a man covers a certain distance at x km/h and an equal distance at y km/h.

Then, the average speed during the whole journey is given by

                 2xy/x+y  km/h

1. 10 students started to eat biscuits. Among them, 1 ate 8 biscuits, 2 of them ate 6 biscuits each, 3 of them ate 4 biscuits each and 4 of them ate 2 biscuits each. The average number of biscuits, each of them ate, was:

A.  4

B.  6

C.  8

D.  3

2. The mean of 11 numbers is 35. If the mean of first 6 numbers is 32 and that of the last 6 numbers is 37, find the sixth number.

A.  27

B.  28

C.  29

D.  30

3. In a 20 over match, the required run rate to win is 7.2. If the run rate is 6 at the end of the 15th over, the required run rate to win the match is:

A.  1.2

B.  13.2

C.  10.8

D.  12

4. The average of 9 integers arranged in a certain order is 32. If the average of the first four integers is 26 and that of the last four integers is 28, then the fifth integer is:

A.  76

B.  72

C.  68

D.  58

5. A batsman has a certain average of runs for 11 innings. In the 12th innings, he makes a score of 90 runs, thereby increasing his average by 5. His average after the 12th innings is:

A.  30

B.  35

C.  40

D.  45

6.The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?

A. 2000

B. 3000

C. 4000

D. 5000

7. In Kiran's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Kiran and he thinks that Kiran's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Kiran?

A. 70 kg

B. 69 kg

C. 61 kg

D. 67 kg

8.A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

A. 28 4/7 years

B. 31 5/7 years

C. 32 1/7 years

D. None of these

9. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the average marks of all the students?

A. 53.23

B. 54.68

C. 51.33

D. 50

10.A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x?

A. 12

B. 5

C. 7

D. 9


 ANSWER AND SOLUTION :

1(A)Explanation:
Total number of biscuits = 1*8+2*6+3*4+4*2= 8 + 12 + 12 + 8 = 40
Average number of biscuits = 40/10= 4

2(C)Explanation:
The sixth number = 6*32 + 6 * 37-11*35
 = 192 + 222 - 385
 = 29

3(C)Explanation:
Total runs required to win the match = 20 * 7.2 = 144
Runs scored in 15 over = 15 * 6 = 90
Runs required in 5 overs = 144 - 90 = 54
Required run rate = 54/5 = 10.8

4(B)Explanation:
Fifth integer = 9*32 - 4*26 - 4*8
= 288 - 104 - 112
= 72

5(B)Explanation:
Let avrage run of 1 innings = x
Total runs of 11 innings = 11x
Score of 12th innings = 90
Average run of 12 innings = x=5
Total runs of 12 innings = 12(x+5)
12(x+5) - 11x = 90
12x + 60 - 11x = 90
x = 30
Thus, average run after the 12th innings = 30+5= 35

6(C)Explanation :
Let the monthly income of A = a
monthly income of B = b
monthly income of C = a
a+b=2×5050---------(Equation1)
b+c=2×6250---------(Equation2)
a+c=2×5200---------(Equation3)
(Equation 1) + (Equation 3) - (Equation 2)
=>a+b+a+c-(b+c)=(2×5050)+(2×5200)-(2×6250)
=> 2a = 2(5050 + 5200 - 6250)
=> a = 4000
=> Monthly income of A = 4000

7 (D)Explanation :
Let Kiran's weight = x. Then
According to Kiran, 65 < x < 72 ------------(equation 1)
According to brother, 60 < x < 70 ------------(equation 2)
According to mother, x = 68 ------------(equation 3)
Given that equation 1,equation 2 and equation 3 are correct. By combining these equations,
we can write as
65<x=68
That is x = 66 or 67 or 68
average of different probable weights of Kiran = (66+67+68)/3=67

8( B)Explanation:
Required average =  (67 x 2 + 35 x 2 + 6 x 3)/(2+2+3)
= (134 + 70 + 18)/7
= 222/7
= 31  5/7 years.

9(B)Explanation :
Average marks of batch1 = 50
Students in batch1 = 55
Total marks of batch1=55×50
Average marks of batch2 = 55
Students in batch2 = 60
Total marks of batch2=60×55
Average marks of batch3 = 60
Students in batch3 = 45
Total marks of batch3=45×60
Total students = 55 + 60 + 45 = 160
Average marks of all the students = ((55×50)+(60×55)+(45×60))/160
=(275+330+270)/16 = 875/16=54.68

10(C)Explanation :
(3+11+7+9+15+13+8+19+17+21+14+x)/12 =12
=>137+x/12=12
=> 137 + x = 144

=> x = 144 - 137 = 7

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Quant Quiz For SSC Exam

Direction (1-10):-Look carefully for the pattern, and then choose which pair of numbers comes next.

1.    28 25 5 21 18 5 14

A.    11 5               

B.    10 7

C.    11 8               

D.    5 10

2.    8 11 21 15 18 21 22

A.    25 18             

B.    25 21

C.    25 29             

D.    24 21

3.    9 16 23 30 37 44 51

A.    59 66             

B.    56 62

C.    58 66             

D.    58 65

4.    2 8 14 20 26 32 38

A.    2 46               

B.    44 50

C.    42 48             

D.    40 42

5.    9 11 33 13 15 33 17

A.    19 33             

B.    33 35

C.    33 19             

D.    15 33

6.    2 3 4 5 6 4 8

A.    9 10               

B.    4 8

C.    10 4               

D.    9 4

7.    17 17 34 20 20 31 23

A.    26 23             

B.    34 20

C.    23 33             

D.    23 28

8.    6 20 8 14 10 8 12

A.    14 10             

B.    2 18

C.    4 12               

D.    2 14

9.    21 25 18 29 33 18

A.    43 18             

B.    41 44

C.    37 18             

D.    37 41

10. 75 65 85 55 45 85 35

A.    25 15             

B.    25 85

C.    35 25             

D.    85 35

Answers with Explanation:-

1. A

Explanation:

      This is an alternating subtraction series with the interpolation of a random number, 5, as every third number. In the subtraction series, 3 is subtracted, then 4, then 3, and so on.

2. B

Explanation:

     This is an alternating addition series, with a random number, 21, interpolated as every third number. The addition series alternates between adding 3 and adding 4. The number 21 appears after each number arrived at by adding 3.

3. D

Explanation:

Here is a simple addition series, which begins with 9 and adds 7.

4. B

Explanation:

This is a simple addition series, which begins with 2 and adds 6.

5. A

Explanation:

     In this alternating repetition series, a random number, 33, is interpolated every third number into a simple addition series, in which each number increases by 2.

6. D

Explanation:

     This is an alternating addition series with a random number, 4, interpolated as every third number. In the main series, 1 is added, then 2 is added, then 1, then 2, and so on.

7. D

Explanation:

      This is an alternating subtraction series with repetition. There are two different patterns here. In the first, a number repeats itself; then 3 is added to that number to arrive at the next number, which also repeats. This gives the series 17, 17, 20, 20, 23, and so on. Every third number follows a second pattern, in which 3 is subtracted from each number to arrive at the next: 34, 31, 28.

8. D

Explanation:

     This is an alternating addition and subtraction series. In the first pattern, 2 is added to each number to arrive at the next; in the alternate pattern, 6 is subtracted from each number to arrive at the next.

9. D

Explanation:

     This is a simple addition series with a random number, 18, interpolated as every third number. In the series, 4 is added to each number except 18, to arrive at the next number.

        10. B

Explanation:

     This is a simple subtraction series in which a random number, 85, is interpolated as every third number. In the subtraction series, 10 is subtracted from each number to arrive at the next.

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Quant Quiz For SSC Exam

1. Thirty men can complete a work in 36 days. In how many days can 18 men complete the same piece of work?

(1) 48   

(2) 36  

(3) 60   

(4) 72 

2. Gaurav spends 50% of his monthly income on household items, 20% of his monthly income on buying clothes, 5% of his monthly income on medicines and saves remaining Rs. 11,250 . What is Gaurav’s monthly income?

(1) Rs. 38,200

(2) Rs. 34,000

(3) Rs. 41,600 

(4) Rs. 45,000

3. The number obtained by interchanging the two digits of a two digit number is lesser than the original number by 54. If the sum of the two digits of the number is 12, then what is the original number?

(1) 28  

(2) 39  

(3) 93  

(4) Can’t say

4. At present Ayushi is eight times her daughter’s age. Eight years from now, the ratio of the ages of Ayushi and her daughter will be 10 : 3 respectively. What is Ayushi’s present age ?

(1) 32 years

(2) 40 years

(3) 36 years

(4) Can’t say

5. In how many different ways can 4 boys and 3 girls be arranged in a row such that all the boys stand together and all the girls stand together?

(1) 75   

(2) 576  

(3) 288   

(4) 24  

6. X can do a piece of work in 20 days and Y can do it in 10 days. They started together, but after 6 days X leaves off. Y will do the rest work in

(1) 1 day  

(2) 2 days 

(3) 7/3 days 

(4) 3 days 

7. A radio is sold for Rs 990 at a profit of 10%. What would have been the gain or loss in percentage had it been sold for Rs 880?

(1) 19/3%  gain 

(2) 17/3% loss 

(3) 17% gain 

(4) 20/9% loss 

8. In an exam, 60% of the total student passed. If the number of failed students is 320 then the total number of students is

(1)600  

(2)700  

(3)800  

(4)900  

9. A cycle is bought for Rs 840 and sold at Rs 920. What is the percentage gain

(1)10.50% 

(2)8.52% 

(3)7.35% 

(4)9.52%

10. If sandeep salary is 30% more than Amar’s salary, the how many percent is Amar’s salary less than that of Sandeep’s?

(1)56%  

(2)23.07% 

(3) 50/3% 

(4)50.6% 

Answers 

1. (3)
Required number of days = (30 * 36)/18 = 60

2. (4)
Let total income of Gaurav be x. Then
(100 – 50 – 20 – 5)% of x = 11250
x = 45000.

3. (3)
Let the number be xy
(10x + y) – (10y + x) = 54
x – y = 6 And  x + y = 12
Solving the equations we get x = 9 and y = 3
So the number is 93.

4. (1)
Let the age of Ayushi’s daughter be x. Then Ayushi’s age is 8x.
(8x + 8)/ (x + 8) = 10/3
x = 4
Ayushi present age = 8x = 32 years.

5. (3)
Required number of ways = 4! * 3! * 2! = 288.


6. 1
(X + Y)’s 6 days’ work = 6 * (1/20 + 1/10) = 9/10
Remaining work = 1 - 9/10 = 1/10
1/10 work is done 2y Y in 10 * 1/10 = 1 day

7. 4
Let the CP is Rs x.
Then, x * 110/100  = 990
x = 900
Now CP is Rs 900 and SP is 880.
% loss =  20/900 * 100 = 20/9%

8. 3
Let the number of student is x out of that 40% have failed.
40/100 * x = 320
x = 320 * 100/40 = 800

9. 4
CP = Rs 840 and SP = Rs 920
Gain = 920 – 840 = Rs 80
gain percentage = 80/840 * 100 = 9.52%

10. 2;
Amar’s salary is less than of Sandeep 2y
(R/100 + R * 100)% = (30/(100 + 30) * 100)%
(30/130 *100 )% = 300/13% = 23% APPROX

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MATH: QUIZ for SSC (Trigonometry)

Answer Key:

 1-(b), 2-(b), 3-(d), 4-(c), 5-(d), 6-(a), 7-(c), 8-(a), 9-(b), 10-(c).

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Types of Questions Asked in Exams on Percentage

TYPE 1.
If there is increase of X% and subsequently X% decrease then there is always loss / decrease in the condition.
 

Example. If rohan salary is increase by 50% and subsequently decrease by 50%. How much percentage loss?
Ans. By trick ----  50x50/100= 25% decrease/loss 

TYPE 2.
if A is P% more than B. then B is less than by A  with P/(100+P)x100 

Example:  If radha earning is 25% more than sita. Then sita earning is how many percentage less then by radha?

Ans. By trick ---- 25/(100+25)x100=20%   

TYPE 3. 
If A is P% less than B. then B is more than by A with P/(100-P)x100 

Example: If golu age is 20% less than gita than gita age is how many percentage more than golu?
Ans. By trick ---- 20/(100-20)x100=25%

TYPE 4.
If there is p% increase in price . how much % decrease his consumption so that his expenditure on it does not change.
formula P/(100+P)x100

Example. If petrol price increase by 25%. How much percentage a person reduced his consumption so that his expenditure on it does not increase? 
Ans. 25/(100+25)x100=20%

TYPE 5.
if there is p% decrease in price . how much % increase his consumption so that his expenditure on it does not change.
formula P/(100-P)x100

Example. If there is 30% decrease in eggs price. How much a person increased his consumption so that his expenditure on it does not increase?   
Ans. 30/(100-30)x100=42.85

TYPE 6.

Example. If suman need 36% minimum mark to passed a exam but she score 24% mark and fail by 9 marks. What is the total mark? 
Ans. Difference in % = difference in mark

In that 36%-24%=12%
that is 12%=9marks
so, total mark = 9/12x100= 75

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Geomatry lines & Angles Notes and Quiz

Dear Readers, 

As you know lines and angles is critical in the study of geometry. Whether we know it or not, we see all sorts of angles on an everyday basis. In order to continue our study of geometry, it will be necessary to learn about the different properties of lines, angles, and their measures. The sections below introduce the different classifications of angles (acute, obtuse, right, or straight).  

Right angle: An angle of 90° is called a right angle.
Acute angle: An angle of less than 90° is called an acute angle.
Obtuse angle: An angle of greater than 90° is called an obtuse angle.
Reflex angle: An angle of greater than 180° is called reflex angle.
Complementary angles: If the sum of the two angles is 90°, then they are called complementary angles.
Supplementary angles:  If the sum of the two angles is 180°, then they are called supplementary angles.
 

Angle Relations: Vertically opposite angles: If two lines intersect each other, then the vertically opposite angles are equal. ∠a = ∠c and ∠b = ∠d
a, c and b, d are vertically opposite angles.

Angles in parallel lines: If a transversal intersects two parallel lines:

 

a. each pair of consecutive interior angles are supplementary.
 ∠4 + ∠5 = 180°
 ∠3 + ∠6 = 180°
b. each pair of alternate interior angles are equal.
 ∠5 =∠3, ∠6 = ∠4
 ∠5 = ∠3 =∠1 =∠7
 ∠6 = ∠4 = ∠2 = ∠8

Collinear: Three or more than three points are said to be collinear, if there is a line which contains them all.  

Concurrent: Three or more than three lines are said to be concurrent, if there is a point which lies on them all.
 

Proportionality Theorem:

In the above diagram, ABBC=DEEF or ACBC=DFEF
 

Quiz on above topics :
1. In the adjoining figure, find ∠ C. If AB // CD

(a) 120 

(b) 50

(c) 110

(d) 100

2. Find the value of x in following figure.

(a) 110

(b) 100

(c) 130

(d) None of these 

3. Find ∠OBD in the given figure. It is given that EC || AO.

(a) 20

(b) 50

(c) 40

(d) None of these 

4. If the two lines n and m are parallel, then find the value of ϕ in the given figure.

(a) 40

(b) 80

(c) 30

(d) None of these 

Answers With Solutions: 
1. (c)

∠ E = 180 - 120 = 60

 

∠ E + ∠ X + ∠ F = 180 ⇒ 60 + 50 + F = 180 ⇒ F = 70
Now ∠ G = 180 - F = 110.
As AB // CD, ∠G = ∠C
So ∠C = 110

  2. (a) 

Sol: As C // E, ∠B = ∠Y

Also ∠Y + ∠Z = 180 ⇒  ∠Z = 180 - 130 = 50

Now in Δ AGF, ∠A + ∠Z + ∠X = 180  ⇒ ∠X = 180 - 20 - 50 = 110

3. (b) 

Sol:   From the diagram, in ΔOBD, 110 + 20 + ∠B = 180 ⇒ ∠B = 50

 

4.(b) 

Sol:  Draw a parellel to n. Now from the diagram ϕ = 50 + 30 = 80 (Alternate interior angles are equal)

 

 

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