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Application Sums
1) The average age of P, Q and R, 3 years ago was 14 years and the average present age of P, Q, R and S together is 20 years. Find the present age of S?
a) 29 years
b) 32 years
c) 36 years
d) 27 years
e) None of these
2) P starts the business with the capital of Rs. 15000. Q joins the business after 4 months and R joins the business after 6 months. At the end of the year, their respective shares are in the ratio of 18: 16: 15. Find the sum of the investment of Q and R together?
a) Rs. 40000
b) Rs. 50000
c) Rs. 55000
d) Rs. 45000
e) None of these
3) The average marks obtained by 65 students in a certain examination are 28. The average marks of passed students is 32 and the average marks of failed students is 12. Then find the total number of passed students?
a) 52
b) 56
c) 48
d) 54
e) None of these
4) Akila borrowed a certain sum of money at simple interest for 4 years at 10 % per annum and he pays Rs. 20000 as interest. Find the compound interest for the same amount at 8 % per annum for 2 years?
a) Rs. 8320
b) Rs. 7860
c) Rs. 8040
d) Rs. 8580
e) None of these
5) Three pipes P, Q and R can fill a tank in 24 hours. After working together for 8 hours, R is closed and P and Q can fill the remaining part in 20 hours. How much time taken by R to fill the tank alone?
a) 100 hours
b) 85 hours
c) 120 hours
d) 105 hours
e) None of these
Data Interpretation
Directions (6 – 10): Study the following information carefully and answer the given questions?
The line graph shows the number of students in three different classes (A, B and C).
A teacher distributes five different stationary items viz. Note, Pen, Book, Pencil and Bag in each class for each student.
In class A, teacher distributes 3 notes, 1 pen, 5 books, x pencil and (x – 1) bag for each student. Total item distributed in the class A is 480.
In class B, teacher distributes 4 notes, y pens, (y + 4) books, (x + 1) pencils and (y – 1) bags for each student. Total items distributed in the class B is twice the total item distributed in the class A.
In class C, total notes distributed by teacher is 10 notes more than total notes distributed in class B and the ratio of total books distributed in class A to C is 2: 3. And then distributes (y + 1) pens, x pencils and z bags for each student.
The teacher distributed a total of 2290 stationary items to all the classes.
6) Quantity I: Find the average number of items distributed in class A
Quantity II: Find the average number of items distributed in class B
a) Quantity I < Quantity II
b) Quantity I = Quantity II
c) Quantity I ≥ Quantity II
d) Quantity I ≤ Quantity II
e) Quantity I > Quantity II
7) What is the ratio of the total pencil to total bags distributed for all the schools together?
a) 7: 9
b) 8: 11
c) 12: 5
d) 6: 7
e) 5: 4
8) Total pen and pencil distributed for school B together is what percentage more/less than the total note and pen distributed in class C together?
a) 20% more
b) 20% less
c) 40% less
d) 25% less
e) 25% more
9) Which of the following stationary items distributed maximum for all the class together?
a) Pen
b) Note
c) Books
d) Pencil
e) Bag
10) What is the difference between the number of Note, pen and bags distributed for all the class together to that of the remaining items distributed for all the class together?
a) 130
b) 180
c) 190
d) 110
e) None of these
Answers :
Directions (1-5) :
1) Answer: A
The average age of P, Q and R, 3 years ago = 14 years
The total present age of P, Q and R = (14 * 3) + 9 = 51 years
The average present age of P, Q, R and S together = 20 years
The total present age of P, Q, R and S together = 80 years
The present age of S = 80 – 51 = 29 years
Shortcut:
Average present age of P, Q and R = 14 + 3 = 17
The present age of S = 20 + (20 – 17) * 3 = 29 years
2) Answer: D
The share of P, Q and R,
= > [15000 * 12]: [Q * 8]: [R * 6] = 18: 16: 15
= > 180000: 8Q: 6R = 18: 16: 15
18’s = 180000
1’s = 10000
8Q = 160000
Q = 20000
6R = 150000
R = 25000
The sum of the investment of Q and R together
= > 20000 + 25000
= > Rs. 45000
3) Answer: A
Let passed students be x,
According to the question,
65 * 28 = 32 * x + 12 * (65 – x)
1820 = 32x + 780 – 12x
1040 = 20x
x = 1040 / 20 = 52
Total number of passed students = 52
(Or)
= > 4 : 1
5’s = 65
1’s = 13
The total number of passed students = 52
4) Answer: A
SI = PNR / 100
20000 = (P * 4 * 10) / 100
P = (20000 * 100) / 40 = Rs. 50000
Compound Interest:
CI for 1st year = 50000 * (8/100) = 4000
CI for 2nd year = 54000 * (8/100) = 4320
CI = 4000 + 4320 = Rs. 8320
Or
CI = P (1 + r/100)n – P
= 50000 (1 + 8/100)2 – 50000
= 58320 – 50000
= Rs. 8320
5) Answer: C
The tank will be filled by P, Q, R in 8 hours = 8/24 = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P and Q to fill the tank = 20/2 * 3 = 30 h
R’s 1 hour work = 1/24 – 1/30 = 1/120
Time taken by R to fill the tank = 120 hrs
Directions (6 – 10):
Class A:
Total notes = 3 * 40 = 120
Total pens = 40 * 1 = 40
Total books = 40 * 5 = 200
Total pencils = 40 * x
Total bags = 40 * (x – 1)
Total item = 120 + 40 + 200 + 40x + 40 (x – 1) = 480
80x – 40 = 120
= > 80x = 160 = > x = 2
Total pencils = 40 * x = 80
Total bags = 40 * (x – 1) = 40
Class B:
Total notes = 60 * 4 = 240
Total pens = 60 * y
Total books = 60 * (y + 4)
Total pencils = 60 * (x + 1) = 60 * (2 + 1) = 180
Total bags = 60 * (y – 1)
Total items = 480 * 2 = 960
240 + 60y + 60y + 240 + 180 + 60y – 60 = 960
600 + 180y = 960
= > y = 360/180 = 2
Total pens = 60 * y = 120
Total books = 60 * (y + 4) = 360
Total bags = 60 * (y – 1) = 60
Class C:
Total notes = 240 + 10 = 250
Total books = 200/2 * 3 = 300
Total pens = 50 * (y + 1) = 50 * (2 + 1) = 150
Total pencils = 50 * x = 50x = 50 * 2 = 100
Total bags = 50 * z
Total items = 2290 – 480 – 960 = 850
250 + 300 + 150 + 100 + 50z = 850
50z = 50
= > z = 1
Total bags = 50 * 1 = 50
6) Answer: A
Quantity I:
Required average = 480/40 = 12
Quantity II:
Required average = 960/60 = 16
Hence, Quantity I < Quantity II
7) Answer: C
Required ratio = 360: 150 = 12: 5
8) Answer: D
Required percentage
= [(250 + 150) – (120 + 180)]/(150 + 250) * 100
= 100/400 * 100 = 25% less
9) Answer: C
Note = 610
Pen = 310
Books = 860
Pencil = 360
Bag = 150
10) Answer: E
Total Note, pen and bags distributed for all the class together
= (610 + 310 + 150) = 1070
Remaining items = 2290 – 1070 = 1220
Required difference = 1220 – 1070 = 150
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