M4maths Previous Puzzles

13 Mar 2019 Width of River

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 60° and 45° respectively. If the bridge is at a height of 9 meter from the banks then find the width of the river? Assume both the banks are at same ground level.

OPtion

1) 14.02 m
2) 14.11 m
3) 14.20 m
4) 14.40 m
5) 14.73 m
6) 14.35 m
7) 14.05 m
8) 14.53 m
9) 14.63 m
10) None of these

Solution

Let A and B be the two sides of the river and C be the point on the bridge. D is a point on straight line between A and B such that CD = 9 meters

Width of the river would = AD+BD

In right angled triangle ACD,
tan 60° = CD/AD
=> √3 = 9/AD
=> AD = 9/√3 = 3√3

In right angled triangle BCD,
tan 45° = CD/BD
=> 1 = CD/BD
=> CD = BD = 9 meters

So the width of the river is AD+BD = 9+3√3 = ~14.20 meters

Correct Option: 3 Best Solution (5)

12 Mar 2019 Word Done

A certain number of men can finish a piece of work in 30 days. If however there were 15 men less it will take 30 days more for the work to be finished. How many men were there originally?

OPtion

1) 15
2) 20
3) 18
4) 24
5) 21
6) 25
7) 26
8) 27
9) 30
10) None of these

Solution

A certain number of men can finish a piece of work in 30 days. If however there were 15 men less it will take 30 days more for the work to be finished.
So the no. of days are doubled (from 30 to 60) , it means no. is men is reduced to half.
so earlier, there were 15*2= 30 men.

Correct Option: 9 Best Solution (0)

12 Mar 2019 Ratio

Initially two cups of same volume are present with milk filled upto 2/7th and 3/7th of their volumes. Water is then filled in both the cups (completely). Then two mixtures are mixed. Find the ratio of water to milk in the mixture?

OPtion

1) 8:5
2) 7:4
3) 5:9
4) 9:5
5) 11:3
6) 5:8
7) 13:9
8) 7:2
9) 5:7
10) None of these

Solution

Let the cups volume be x.
here we assume that water fills both volumes completely
after mixing , total milk is -> 2/7x + 3/7x = 5/7x
after mixing , total water is -> 5/7x + 4/7x = 9/7x
therefore water to milk ratio is (9/7)/(5/7) = 9:5

Correct Option: 4 Best Solution (0)

11 Mar 2019 Code Written

A programmer has the capability of thinking 70 lines of code in six minutes and can type 70 lines of code in 12 minutes. He takes a break for six minutes after every 12 minutes. How many lines of codes will he complete writing in 72 minutes?
Assume that he always needs to think before writing any code?

OPtion

1) 250
2) 165
3) 180
4) 150
5) 135
6) 175
7) 155
8) 200
9) 210
10) None of these

Solution

6-think
6-type
6-break
6-type
6-think
6-break
6-type
6-type
6-break
6-think
6-type
6-break


So five times for 6 minutes he types/writes code, total minutes he spends typing the code = 6*5 = 30 minutes
In 12 Minutes he can type 70 lines of code
In 30 minutes he types (70/12)*30 = 175 lines

Correct Option: 6 Best Solution (3)

08 Mar 2019 Distance Traveled

A tempo, while travelling at 75 kmph, uses 25% more petrol than it uses while travelling at 50 kmph for travelling a certain distance. Using one liter of petrol, it can travel 22.5 km at 50 kmph. How far can the tempo travel on 15 liters of petrol at a speed of 75 kmph?

OPtion

1) 180
2) 220
3) 240
4) 260
5) 270
6) 280
7) 300
8) 320
9) 330
10) None of these

Solution

At 50kmph
22.5 KM is traveled with 1 liter petrol
1 KM is traveled with 1/22.5 liter

At 75 KMPH
It uses 25% extra petrol
So 1 KM is traveled with 1.25*1/22.5 liter

Distance traveled with 15 liters @ 75 KMPH = 15* 22.5/1.25 = 270 KM

Correct Option: 5 Best Solution (0)

07 Mar 2019 Envelopes Used

An Office used three types of envelopes: small,medium and large. They used 160 small envelopes. The no.of Medium envelopes used was 5 times the no. of small envelopes plus 5/20 of the total number of envelopes. The no. of large envelopes was equal to the no. of small envelopes plus 5/20 of the no. of medium envelope. Altogether, How many envelope did they use?

OPtion

1) 1600
2) 2280
3) 3280
4) 2640
5) 1540
6) 1280
7) 1640
8) 1840
9) 1920
10) None of these

Solution

Let the total no. of envelopes be x

No. of small envelopes = 160
No. of medium envelopes =5*160+5/20*x = 800+5/20*x
No. of large envelopes = 160 +5/20(800+5/20*x) = 360 + 25/400*x

Sum of small, medium and large envelopes = x

160 + 800 + 5/20*x + 360 + 25/400*x = x
1320 + 125/400*x = x
1320*x + 5/16 = x
=> 11/16 x = 1320
x = 1920

Correct Option: 9 Best Solution (0)

06 Mar 2019 Age

At the time of marriage, a man was 5 years elder to his wife. 16 years after their marriage, his age is 8/7 times the age of his wife. What was wife's age at the time of marriage ?

OPtion

1) 16
2) 27
3) 17
4) 19
5) 20
6) 21
7) 22
8) 23
9) 24
10) None of these

Solution

let wifes age= x
husband age = x+5
now after 16 years of marriage
Wife's age = x+16
Husband's age = x+16+5 = x+21


8/7(x+16)=x+21
=> 8x+16*8 = 7x+21*7
Solving we get = 19

Correct Option: 4 Best Solution (0)

05 Mar 2019 GP

If the second term of a G.P. is 9 and sum of the infinite terms is 40.5, then what will be the 3rd term?
Given that the first term is greater than 14.

OPtion

1) 4.5
2) 6
3) 7.5
4) 1.5
5) 1.0
6) 3.0
7) 3.5
8) 2.5
9) 0.333
10) None of these

Solution

nth term = a * r ^ (n-1)
=> For 2nd term => 9 = a*r^(2-1)
=> 9 = ar
=> r = 9/a

Sum of infinite terms in G.P = a/(1-r)

Sum of infinite terms in G.P => 40.5 = a/(1-r)
=> 40.5 - 40.5r = a
=> 40.5 = a + 40.5*9/a
=> 81a = 2a^2 + 729

Solving we get a = 27 or 13.5
As the first term is greater than 15, hence 13.5 is ruled out

So r = 9/27 = 1/3

Hence 3rd term => 27*(1/3)^(3-1) = 27*(1/3)^2 = 27/9 = 3

Correct Option: 6 Best Solution (7)

04 Mar 2019 Percentage

A person spends 20% of his salary on food, 35% on house rent, 20% on conveyance and 10% of the remaining on entertainment. If his savings at the end of the month is Rs. 23700, then his salary per month in rupees is:

OPtion

1) 158600
2) 158100
3) 158200
4) 158300
5) 158000
6) 158500
7) 158680
8) 158700
9) 158800
10) None of these

Solution

Food 20%
Rent 35%
Coveyance 20%
Entertainment 10%
Saving% 100 - (20+35+20+10) = 15%

Saving Amount 23700

15% of salary = 23700
100% of salary = 23700*100/15

So Salary 158000

Correct Option: 5 Best Solution (0)

01 Mar 2019 Even Number

How many factors of 997972488 are even numbers?

OPtion

1) 125
2) 75
3) 120
4) 135
5) 60
6) 75
7) 180
8) 150
9) 90
10) None of these

Solution

997972488 = 73^2 * 17^2 * 3^4 * 2^3

Any factor of this number should be of the form 73^a * 17^b * 3^c * 2^d

For the factors of this number to be an even number d should be non 0

a can take values 0, 1, 2
b can take values 0, 1, 2
c can take values 0, 1, 2, 3, 4
d can take values 1, 2, 3


Total number of odd factors = 3*3*5*3= 135



Option 4)

Correct Option: 4 Best Solution (1)