M4maths Previous Puzzles

17 Jan 2019 Number

A number consists of 3 digits whose sum is 10. The middle digit is equal to the difference of the other two and the number will be increased by 99 if its digits are reversed. The square of the number is:

OPtion

1) 164036
2) 168100
3) 180625
4) 172225
5) 264196
6) 254016
7) 164025
8) 180616
9) 179776
10) None of these

Solution

let the digits of the No. be x. y & z
Hence, x+y+z=10.................(1)
z-x=y..............(2)

AS per the condition
(100z+10y+x)-(100x+10y+z)=99
=> z-x=1 -----(3)

Form (2) and (3), we deduce y=1

From equation (1) and (2)
we get,
x+z=9 and
z-x =1

Solving we get z= 5 and x = 4

So the number is 415 and its square is = 172225

Correct Option: 4 Best Solution (0)

16 Jan 2019 Population

The population of rodents in a house doubles every day. Every day 25 rodents are killed. How many rodents are there if after every four days, the number of rodents becomes same again?

OPtion

1) 20
2) 5
3) 15
4) 6
5) 24
6) 12
7) 25
8) 16
9) 8
10) None of these

Solution

1st day - x
2nd day - (2x-25)
3rd day - [2(2x-25)-25]
4th day - 2[2(2x-25)-25] - 25 = 8x - 7*25

After fourth day the value becomes equal to the first day so 8x - 7*25 = x
Solving, we get x = 25

Correct Option: 7 Best Solution (0)

15 Jan 2019 Profit & Loss

Lalu sold his watch and sunglasses at a loss of 5% and gain of 5% respectively for 3600 to Bhalu. Bhalu sold the same sun glasses and watch at a loss of 4% and gain of 4% respectively for 3800. The price of watch and sun glasses respectively to Lalu in rupees were.

OPtion

1) 2650, 950
2) 2550, 1050
3) 2750, 850
4) 2850, 850
5) 2450, 1250
6) 2950, 750
7) 2450, 1050
8) 2650, 1050
9) 2850, 950
10) None of these

Solution

Let the CP of watch be Rs x and sunglasses be Rs y.

Lalu sold his watch and sunglasses at a loss of 5% and gain of 5% :
3600=95x/100 + 105y/100

Bhalu sold the same sun glasses and watch at a loss of 4% and gain of 4% respectively :
3800= 104x/100 + 96y/100

On solving,
y=744.44
x=2966.67

Option 10)

Correct Option: 10 Best Solution (0)

14 Jan 2019 Simple Interest

Nirav took a loan of Rs. 201900 from PNB with simple interest for as many years as the rate of interest. If he was supposed to pay Rs. 395724 as interest at the end of the loan period, what was the rate of interest?

OPtion

1) 11
2) 10
3) 11.5
4) 12.5
5) 14.5
6) 15
7) 16
8) 14.0
9) 15.5
10) None of these

Solution

SI = PRT/100
=> 395724 = (201900 *R*T)/100
As R=T so => 395724 = (201900 *R*R)/100

R^2 = 395724 * 100/201900 = 196
=> R= 14

Option 8)

Correct Option: 8 Best Solution (0)

11 Jan 2019 Speed and Distance

Rahmatullah could either walk or drive to office. The time taken to walk to the office is 11 times the driving time. One day, his wife took the car making him walk to office. After walking 2.5 km, he reached a temple when his wife called to say that he can now take the car. Ramanujam figured that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office in KMs.

OPtion

1) 5/2
2) 5/3
3) 7/2
4) 7/3
5) 2.0
6) 2.5
7) 6/2
8) 3.5
9) 3.25
10)None of these

Solution

Suppose the distance between his home and office is x km. Then, distance between his office and temple is (x – 2.5) km.
If he walks at a speed of y km/hr. Then his driving speed = 11y km/hour, as he is 11 times faster in car.

Then,
2.5/y + x/11y = (x – 2.5)/y
Or, 2.5 + x/11 = x – 2.5
or 10x/11 = 5
Or, x = 11/2
Finally, x – 2.5 = 11/2-5/2 = 6/2 = 3
Option 7)

Correct Option: 7 Best Solution (4)

10 Jan 2019 Stocks

The market value of a 8.5% stock, in which an income of Rs. 1900 is derived by investing Rs. 11000, brokerage being 1/4 %, is:

OPtion

1) 48.25
2) 48.75
3) 49.00
4) 49.21
5) 48.50
6) 48.96
7) 48.85
8) 48.45
9) 48.60
10) None of these

Solution

For an income of Rs. 1900, investment = Rs. 11000

For an income of Rs. 8.5, investment = Rs. (11000/1900) * 8.5 = 49.21
For a Rs. 100 stock, investment = Rs. 49.21

Market value of Rs. 100 stock = Rs. 49.21 - 0.25 = Rs. 48.96

Option 6)

Correct Option: 6 Best Solution (0)

09 Jan 2019 Percentage

If P is 60% of Q, Q is 50% of R; R is 40% of S, S is 45% of T. Find P: T ?

OPtion

1) 3/50
2) 3/25
3) 7/50
4) 8/25
5) 4/25
6) 27/1000
7) 27/250
8) 27/500
9) 27/2000
10) None of these

Solution

P = 0.6 Q
Q= 0.25 R
So P = 0.6*0.25 R
R = 0.4 S
So, P = 0.6*0.5 * 0.4 S
S = 0.45*T
Again, P = 0.6* 0.5 * 0.4 * 0.45*T = 54/1000T
So P/T = 27/500
Option 8)

Correct Option: 8 Best Solution (5)

08 Jan 2019 Ratio

Isha’s grandfather was 5 times older to her 4 years ago. He would be three times of her age 8 years from now. 7 years ago, what was the ratio of Isha’s age to that of her grandfather’s age?

OPtion

1) 2:5
2) 1:6
3) 1:4
4) 3:19
5) 3:17
6) 5:23
7) 4:7
8) 4:19
9) 5:18
10) None of these

Solution

Suppose Isha's grandfathers age is x and Isha's age is y

4 years ago
x-4 = 5*(y-4)
=> x = 5y - 16 --(i)

8 years from now
x+8 = 3*(y+8)
=> x = 3y + 16 --(ii)

(i) = (ii)
5y - 16 = 3y + 16
=> 2y = 32
=> y = 16
So x = 64

7 years ago
Age of Grandfather = 64 - 7 = 57
Age of Isha = 16-7 = 9
Ratio of ages = 9:57 = 3 : 19


Option 4)

Correct Option: 4 Best Solution (8)

07 Jan 2019 Age

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 55 years now, what would be the son's age 4.5 years later?

OPtion

1) 31
2) 30
3) 32
4) 29
5) 28
6) 23
7) 24
8) 25
9) 26
10) None of these

Solution

Let the sons current age be x
So fathers age x years back when son was born => 55-x = x
Solving we get x = 27.5
4.5 Years later son's age = 27.5 + 4.5 = 32 years

Option 3)

Correct Option: 3 Best Solution (11)

04 Jan 2019 Lift

Jack enters a lift on the 25th floor, which is going up @ 56 floors/min speed. At the same time Jill enters another lift on the 70th floor which is going down @ 64 floors/min speed. At what floor will

they be together?

OPtion

1) 41
2) 42
3) 43
4) 44
5) 45
6) 39
7) 47
8) 46
9) 48
10) None of these

Solution

Relative Speed = 56+64 = 120 floors/min
Relative Distance = 70 - 25 = 45 floors

Time to cover 45 floors = 45*60/120 = 22.5 seconds

Floors travelled by Jack in 22.5 seconds = (56/60)*22.5 = 21
Floors on which they will meet = 25 + 21 = 46th
Option 8)

Correct Option: 8 Best Solution (7)