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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