# Aptitude model placement papers with solution - set 1

## Aptitude model placement papers with solution - set 1

Q1. The present age of Arjun is such that if 6 years is subtracted from his age and the remainder divided by 18, we get Ramesh’s age. Now if Ramesh is 2 years younger to Dhruv who is presently 5, find out Arjun’s present age.

A. 50
B. 55
C. 62
D. 60

Solution: According to the question Dhruv's current age is 5 years. So Ramesh's age will be 3 years.

Let Arjun's age be x.

From the given data we can implicate that:

(x-6)/18 = Ramesh's age = 3 years

=> x-6 = 54

=> x = 60 years.

Q2. A rectangular play ground with dimensions of 40m X 60m has two concrete crossroads in between with the rest of it being used as lawn. The lawn area is 2109 sq m. What is the width of the crossroad?

A. 2 meters
B. 3 meters
C. 4 meters
D. 5 meters

ANSWER: B. 3 meters
Solution: Area of the rectangular playground = Length x Breadth = 40 meter * 60 meters

Park area= 40X60= 2400 metres. This implies that area of crossroads = Lawn area - Park area

Area of cross roads= 2400 metres -2109 metres ( Given )

Now let width of cross roads be x

Therefore, Total area of cross road= (x * 40) + (x * 60) – x²

{ Area of horizontal crossroad + Area of vertical crossroad - Area of middle added twice }

=>291 = 100x - x²
=>Solving for x, x = 3m

Q3. Following data represents the total sales for a fruit seller in 5 months respectively:
Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 to get an average sale of Rs 6500 what must be his sale in the 6th month?

A. 4800
B. 4991
C. 5004
D. 5000

Solution: Let the sale in 6th month be x.

=> Average is to be made Rs 6500 at the end of 6th month:

Therefore, (6435 + 6927 + 6855 + 7230 + 6562 + x)/6 = 6500

=> Hence, 34009 + x = 39000

x = 4991

Q4. In a year the first day is Friday. Assuming that it is not a leap year, what is the last day of the year?

A. Monday
B. Wednesday
C. Thursday
D. Friday

Solution: It is given that it is not a leap year.

A normal year contains 365 days which can be divided into 52 weeks and 1 day.

=> Total odd days = 1

=> First day of the year is Friday

First day of next year: Friday + 1 day = Saturday.

Hence, last day of the year = Friday

Q5. 5/8th of a job is completed in 10 days. If a person works at the same pace, how many days will he take to complete the job?

A. 4

B. 5

C. 6

D. 7

Solution: It is given that 5/8th of the work is completed in 10 days.

=> Remaining work = 3/8th of total

Applying unitary method:

Total work will be completed in 10 * 8 / 5 days

=> It takes 16 days to complete total work

=> Hence, remaining work days = 16 - 10 = 6 days

Q6. The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 540. What is the banker's discount?

A. 1240
B. 1120
C. 1190
D. 1290

Solution: In a problem related to banker's discount:

Total Discount (TD) = Bankers Gain (BG) X 100 / (Rate x Time)

Here Total discount = 540

Rate = 12%

Time = 6 years

Therefore, Applying the formula: TD = 540 X 100/(72)

=> TD = 54000/172 = 750

=> Bankers Discount = 750 + 540 = 1290 Rs

Using the formula: total discount= bankers discountX100/ present worth

Substituting and solving, 540=BD-750

BD= 1290 Rs

Q7. A clock is started at 12 Noon. By 10 minutes past 5, what angle is covered by the hour hand?

A. 155 Degrees
B. 150 Degrees
c. 145 Degrees
D. 152 Degrees

ANSWER: A. 155 Degrees

Solution: According to the question the clock is started at 12.

Angle covered by the hour hand in 12 hours = 360 degrees

Angle covered by hour hand in 5 hours = 360 x 5 / 12 = 150 degrees.

=> Now, in one hour the hour hand turns 30 degrees.

In 10 minutes the hour hand will turn 30/6 degrees = 5 degrees

=> Angle traced by hour hand in 5 hour 10 minutes = 150 + 5 degrees = 155 degrees

Q8. If in a certain code 3 * 4 = 25 and 6 * 8 = 100 then what is the value of 12 * 5?

A. 144
B. 169
C. 154
D. 178

Solution: In this question the pattern * represents a code.

=> 3² + 4² = 25

=> 6² + 8² = 100

=> 12² + 5² = 169

Q9. As a product of primes, how can you express 504?

A. 2 × 2 × 3 × 3 × 7 × 7
B. 2 × 3 × 3 × 3 × 7 × 7
C. 2 × 3 × 3 × 3 × 3 × 7
D. 2 × 2 × 2 × 3 × 3 × 7

ANSWER: D. 2 × 2 × 2 × 3 × 3 × 7

Solution: Simple HCF techniques need to be applied in the question:

504 can be represented as 2 x 2 x 2 x 3 x 3 x 7

Q10. From a point P, a man sees a top of the tower making an angle of elevation of 30 degrees with his eyes. After walking some distance, the angle now subtended is 45 degrees. What is the distance between the base of tower and point P?

A. 9 units
B. 12 units
C. 33 units

Solution: This is a simple problem involving heights and distances.

Initially the man sees top of a building at the angle of elevation of 30 degrees.

=> Tan 30 = Height of the building (Y)/Distance from the building (X)

After walking an unknown distance the angle now subtended is 45 degrees.

=> Tan 45 = Height of the building (Y)/ New distance from the building (Z)

These are 2 equations and 3 unknown variables.