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Q1. The Speed of a boat (kmph) in still water is numerically equal to 1 / 4th of perimeter of a circle whose radius is 7 m. The speed of the stream is x kmph. An average age of a family is x years. Which consist of four persons and their ratio of ages are 2:3:4:5. The 2nd youngest person age is 6 years. The distance traveled by the boat through downstream in 5 hours is numerically equal to selling price (in Rs) of an item. If the seller face loss of 10% what is the cost price of the item?

a) Rs.200
b) Rs.150
c) Rs.100
d) Rs.250
e) Rs.175

Q2. A man go to his office from his home at 5kmph more than normal speed he will reach office in 20 minutes earlier. If he goes to his office at 10km/hr less than normal speed he will reach office 80 minutes later. The time taken to cover the distance with normal speed is equal to time taken by a tap to fill a tank. The tap fills 30 litres per minute. The capacity of the tank is x litres. An area of a square is x m2. Perimeter of the square is numerically equal to average of five consecutive even numbers. Find the difference between the smallest number and cube of 6.

a) 15
b) 25
c) 10
d) 20

e) None of these

Q3. The speed of a boat in downstream and upstream is 40km/hr and 2x km/hr respectively. The speed of the stream is x km/hr. A, B and C can do a piece of work in x, 2x and 3x days respectively. Initially, the least efficient person worked for 3 days and then left. Then B worked for 4 days and left. The remaining work was completed by the most efficient person in y days. A shopkeeper mixes x kg of variety 1 rice cost of Rs.3y/kg with y kg of variety 2 rice cost of Rs.2x/kg , sold the mixture at a price of Rs.z/kg and he did not get any profit. The cost price of a product is Rs.34z and gains x% when offers discount of 23%. Selva invests Rs.510z at simple interest of x% per annum for 4 years in bank A and then he withdraws all the money from bank A to invest in bank B which offers compounded half yearly of x% per annum for 1 year. Find the difference between the interest received from bank A and B together and the marked price of the product.

a) Rs.5706.25
b) Rs.7060.75
c) Rs.4706.75
d) Rs.6406.75
e) Rs.6555.75

Q4. There are four persons A, B, C and D are sitting in a row. All are facing north. All of them has different ages 20yrs, 25yrs, 30yrs and 35yrs, but not necessarily in the same order. The number of persons sits between A and B is same as between C and D. A is not an immediate neighbour of B and D. The age of A is 30 yrs. The sum of the age of B and C is numerically same as the number of days taken by Arul to complete a piece of work. Arul and Bala together can complete the same work in 20 days. Bala can complete the same work in x days. 70% of its usual speed, a train of length 10x m crosses a platform of length 190m in 7 seconds. At its normal speed, the train crosses a pole in 3 seconds.  The age of one who sits third to the right of A is z years. How many different straight lines can be formed by joining ‘z’ different points on a plane of which 4 are collinear and the rest are non-collinear?
a) 184
b) 190
c) 185
d) 181

e) 180

Direction:

In Chennai Anna University, the first year is a foundation program for all the students after which in second year the students can-opt for their major subject. In 2015, only 80% of the students passed the first year examination and all of those who passed joined in the second year. In 2015, only 20% of students of first year who passed the first year examination joined physical sciences, 30% joined the Arts stream, 40% joined commerce stream while others joined computer stream. Apart from those, some students from other universities who passed their first year also joined Chennai Anna University. Such students were 30% of the number of first year students from Chennai Anna University who passed 2015 examination. The number of students from other universities across physical sciences, Arts, commerce and computer streams are joined in Chennai Anna University were in ratio 1: 3: 4: 2 respectively. In 2015, the number of students in Arts stream in Chennai Anna University in second year was 780.

Q5. In 2015, what percent of science stream students in second year in Chennai Anna University were first year science stream students who pass-outs from Chennai Anna University only? (Approximately)

(A) 87%
(B) 83%
(C) 92%
(D) 77%

(E) 73%

Q6. Q6.What is the total number of students promoted to second year?
(A) 2500
(B) 2250
(C) 2000
(D) 1500
(E) 1750

Q7. What is the total number of students studying in Chennai Anna University in second year?
(A) 2000
(B) 2600
(C) 2300
(D) 2700

(E) 2400

Q8. What was the number of students in second year commerce stream in Chennai Anna University in 2015?
(A) 1040
(B) 1080
(C) 1050
(D) 1150
(E) 1200

Q9. What is the number of students from other universities joining Chennai Anna University in 2015?

(A) 2500
(B) 2600
(C) 2800
(D) 2400
(E) 1000

Q10. A Shopkeeper sells laptops at the rate of Rs 457 each and earns the commission of 4%. He also sells Mobile phones at the rate of Rs 80 each and earns a commission of 20%. How much amount of commission will he earn in two weeks if he sells 10 laptops and 6 mobile phones per day?

a) Rs 270.0
b) Rs 298.7
c) Rs 382.1
d) Rs 399.8
e) None of these

Solution:

Q1. SOL:   C

Perimeter of the circle = 2πr² ×(22/7) ×7=44cm
Speed of the boat in still water = 14 ×44=11 kmph
Average age of family = x
Ratio of the ages of family = 2x:3x:4x:5x
2nd youngest person age = 3x = 6; x=2
Average age of the family = (1/4) x 4=(28/4)=7
Speed of the stream = 7kmph
The downstream of the boat = 11+7 = 18kmph
Distance travelled by boat in 5 hours = 18 × 5=90km
Selling price of an item = Rs 90
Cost price = 90 ×(100/90)=Rs 100

Q2. SOL:   D

Let distance and original speed of man be ‘d’ km and ‘s’ km/hr respectively
d/s – d/(s+5) = 20/60 - - -  -(i)
d/(s-10) – d/s = 80/60 - - - - (ii)
On solving above two equations we get,
d= 50 and s = 25
Time taken with normal speed = 50/25 = 2hr
Tank filled by tap in 2 hours
Capacity of tank =30×120=3600 litres
Area of the square = 3600 m2
Side of the square = 60 m
Perimeter of the square = 4a =4×60=240m
Five consecutive even numbers are x, x+2, x+4, x+6 and x+8
Sum of numbers =240×5=1200
5x + 20 = 1200
X = 236
Required difference = smallest number – 63 = 236 – 216= 20

Q3. SOL:   C

Speed of the stream,
(40- 2x) = x
X = 10 km/hr
A, B and C can do the work in 10, 20 and 30 days.
Total units = 60 (LCM of 10, 20 and 30)
A = 6 units/day
B = 3 units/day
C = 2 units/day
Least efficient person is C worked for  3 days then 3× 2 = 6 units completed
B worked for 4 days then 4 × 3 = 12 units completed
Remaining 42 units completed by A in (42/6)=7 days
Y = 7 days

(20-z)/(z-21) = 10/7
Z = 350/17
The cost price of the product = 34×(350/17)=Rs.700
Marked price = 700×(110/100)X (100/77) =Rs.1000
Principle is 510×(350/17) =Rs.1050
Bank A,
10500×4×(10/100)=Rs.4200
Bank B,
(10500+4200) ((1+(5/100))²-14700=1506.75
Required difference = (4200+ 1506.75) – 1000 = Rs.4706.75

Q4.  SOL:   C

Usual speed of the train be S km/hr
70% of S = (10x+190)/7
S =(10x / 3)
70% of (10x / 3)=(10x +190)/7
X = 30
Therefore, Bala can complete the work in 30 days.
Arul’s per day work =1/20 – 1/30 = 1/60

Therefore, Arul can complete the work in 60 days.
Hence, the sum of the ages of B and C is 60 years.
Therefore, we can find the age of D is 20 years because age of A is 30 years remaining given age is 25 years, 30 years and 35years out of three the sum of the two is 60 years so that should be 25 years and 35 years.

Hence value of z is 20
Straight line can be formed by joining 2 points
Total number of lines formed by 20 points = 20c2

Number of lines formed by 4 points =4C2
But it also includes that in which 4 points are in straight line. From those 4 points only one line can be formed.

Required number of lines = 20C2  - 4C2 + 1 = 185

Q5. SOL:  A

Let us assume the total number of first year students in Chennai Anna university be X
Then, as per data, number of students who passed in first year = 0.8X
Students in physical science, commerce, arts and computer stream becomes: 0.16X, 0.32X, 0.24X, 0.08X respectively.
Total number of students from other universities = 30% of 0.8X = 0.24 X
Ratio of students from other universities in different streams is
Physical Science = 0.024X, Arts = 0.072X, Commerce = 0.096X, computer = 0.048X
Given that number of students in arts stream = 780
Therefore,
0.072X+ 0.24X = 780
X= 2500
Hence, total number of students in first year = 2500
Total students in promoted to second year = 2000
Students from other Universities joining Chennai Anna University = 0.24X = 600
Total students studying in Chennai Anna University in second year = 2000+ 600 = 2600
Total science students in Chennai Anna University = 0.16x+0.024x = 460
First year pass- outs of Chennai Anna University joining science stream = 0.16X = 400
Required % = (400/460)×100=87%

Q6.  SOL:   C

Let us assume the total number of first year students in Chennai Anna university be X
Then, as per data, number of students who passed in first year = 0.8X
Students in science, commerce, arts and computer stream becomes: 0.16X, 0.32X, 0.24X, 0.08X respectively.
Total number of students from other universities = 30% of 0.8X = 0.24 X
Ratio of students from other universities in different streams is
Science = 0.024X, Arts = 0.072X, Commerce = 0.096X, computer = 0.048X
Given that number of students in arts stream = 780
Therefore,
0.072X+ 0.24X = 780
X= 2500
Hence, total number of students in first year = 2500
Total students in Anna University promoted to second year = 2000

Q7. SOL:   B

Let us assume the total number of first year students in Chennai Anna university be X
Then, as per data, number of students who passed in first year = 0.7X
Students in Physical science, commerce, arts and computer stream becomes: 0.16X, 0.32X, 0.24X, 0.08X respectively.
Total number of students from other universities = 30% of 0.8X = 0.24 X
Ratio of students from other universities in different streams is
Physical Science = 0.024X, Arts = 0.072X, Commerce = 0.096X, computer = 0.048X
Given that number of students in arts stream = 780
Therefore,
0.072X+ 0.24X = 780
X= 2500
Hence, total number of students in first year = 2500
Total students in promoted to second year = 2000
Students from other Universities joining Chennai Anna University = 0.24X = 600
Total students studying in Chennai Anna University in second year = 2000+ 600 = 2600

Q8. SOL:   A

Let us assume the total number of first year students in Chennai Anna university be X
Then, as per data, number of students who passed in first year = 0.8X
Students in Physical science, commerce, arts and computer stream becomes: 0.16X, 0.32X, 0.24X, 0.08X respectively.
Total number of students from other universities = 30% of 0.8X = 0.24 X
Ratio of students from other universities in different streams is
Physical Science = 0.024X, Arts = 0.072X, Commerce = 0.096X, computer = 0.048X
Given that number of students in arts stream = 780
Therefore,
0.072X+ 0.24X = 780
X= 2500
Hence, total number of students in first year = 2500
Total students in Anna University promoted to second year = 2000
Students from other Universities joining Chennai Anna University = 0.24X = 600
Total students studying in Chennai Anna University in second year = 2000+ 600 = 2600
Total number of students in commerce stream in 2015 = 0.32X+0.096X = 0.416X = 1040

Q9. SOL:   B

Let us assume the total number of first year students in Chennai Anna university be X
Then, as per data, number of students who passed in first year = 0.8X
Students in science, commerce, arts and computer stream becomes: 0.16X, 0.32X, 0.24X, 0.08X respectively.
Total number of students from other universities = 30% of 0.8X = 0.24 X
Ratio of students from other universities in different streams is
Science = 0.024X, Arts = 0.072X, Commerce = 0.096X, computer = 0.024X
Given that number of students in arts stream = 780
Therefore,
0.072X+ 0.24X = 780
X= 2500
Hence, total number of students in first year = 2500
Total students in promoted to second year = 2000
Students from other Universities joining Chennai Anna University = 0.24X = 600
Total students studying in Chennai Anna University in second year = 2000+ 600 = 2600

Q10. SOL:   E

SP of laptop= Rs 457
Commission on one laptop=(4×457)/100
Commission on 10 laptops=(4×457×10)/100=Rs 182.80
SP of mobile= Rs 80
Commission on one mobile=(8×20)/100
Commission on 6 mobiles=(8×20×6)/100=Rs 96.00
Total commission on one day= (Rs 182.8+96) = 278.80
The amount of commission will he earn in two weeks = 278.8 ×14 = Rs.3903.2

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