M4maths Previous Puzzles

04 Mar 2022 Probability

If 40% of the students of a class like football, 75% of the students like basketball, and 30% like both. If a student is picked at random who likes at least one of these games, what is the probability that he likes only football?

OPtion

1) 15/17
2) 2/13
3) 4/13
4) 9/17
5) 9/13
6) 8/13
7) 3/17
8) 8/17
9) 2/17
10) None of these

Solution

% of students who likes only football=40-30=10
% of students who likes at least one game=40+75-30=85
Required probability = P(Students likes only football) / P(Students who likes at least 1 game) = 10/85 = 2/17

Correct Option: 9 Best Solution (2)

03 Mar 2022 Time Distance & Speed

The speed of the train is two more than twice of the time taken to cover 1012 km at uniform speed. What is the ratio of the values of time taken to cover the distance and speed of the train?

OPtion

1) 3 : 5
2) 3 : 7
3) 7 : 15
4) 23 : 48
5) 10 : 21
6) 12 : 25
7) 13 : 24
8) 11 : 23
9) 13 : 27
10) None of these

Solution

Let time taken to cover distance=t, then Speed=(2+2t)
Distance = Speed x Time
1012 = (2+2t) x t
t² + t - 506 = 0
(t+23) (t-22) = 0
t= -23 or 22
Considering +ve value of time t=22
.'. Speed=(2+2x22)=46
Hence required ratio of time and speed = 22/46 = 11/23

Correct Option: 8 Best Solution (3)

02 Mar 2022 Time and Work

A construction company employs 60 men to build a bridge of 500 m in 30 days working 8 hours a day. If in 24 days they completed 3/5 part of work, then how many more employees should be hired to finish the work in time, working 10 hours a day?

OPtion

1) 36
2) 45
3) 68
4) 52
5) 58
6) 72
7) 66
8) 56
9) 60
10) None of these

Solution

Work completed by 60 men in 24 days, working 8 hrs/day=3/5, so remaining work=(1 - 3/5)=2/5
Let 'x' more men are employed to complete the remaining work in 6 days, working 10 hrs/day
Then, according to Men, days & work formula
60 men * 24 days * 8 hrs / (3/5) = (60+x) men * 6 days * 10 hrs / (2/5)
128 = (60+x)
x = 68

Correct Option: 3 Best Solution (0)

01 Mar 2022 Geometry

Two distinct pints (a,b) and (b,c) lie on the line y = -x + 5. What is the value of (a - c) ?

OPtion

1) 2
2) -3
3) -1
4) 0
5) 1
6) b²
7) -2b
8) b
9) 2b
10) None of these

Solution

Since (a,b) and (b,c) lie on the line, the slope of the line is (c -b) / (b - a).
Equation of the line y = mx + b, where m=slope and b= y intercept
Given equation of line y = -x + 5 gives m=-1
.'. Slope of the line (c -b) / (b - a) = -1
c - b = -b + a
a - c = 0

Correct Option: 4 Best Solution (3)

28 Feb 2022 Profit and Loss

By selling an article for Rs. 171, a shopkeeper gains as much percent as the cost price of an article. In order to get 40% profit, at what price (Rs.) he should sell an article ?

OPtion

1) 112
2) 136
3) 120
4) 116
5) 131
6) 141
7) 126
8) 131.25
9) 157.25
10) None of these

Solution

Let the CP of an article be Rs. x, then x + x*x/100 = 171
x^2 + 100x - 17100 = 0
(x-90) (x+190) = 0
x = 90
.'. The selling price at 40% profit = 90*(140/100) = 126 Rs.

Correct Option: 7 Best Solution (2)

25 Feb 2022 Sequence & Series

Fractions 1/(x+9) , 1/(x+13) and 1/(x+21) are in arithmetic progression, then x=?

OPtion

1) 8
2) 10
3) 7
4) 3
5) 4
6) 5
7) 6
8) 12
9) 2
10) None of these

Solution

For an A.P. difference between two consecutive terms is same.
.'. 1/(x+9) - 1/(x+13) = 1/(x+13) - 1/(x+21)
[(x+13) - (x+9)] / [(x+9)(x+13)] = [(x+21) - (x+13)] / [(x+13)(x+21)]
4/(x+9) = 8/(x+21)
x = 3

Correct Option: 4 Best Solution (5)

24 Feb 2022 Time Distance & Speed

In a race of 1.6 km, if A allows B a start of 160 m and the ratio of the speeds of A and B is 10:9, then which one of the following is correct?

OPtion

1) A wins by 20 m
2) A wins by 40 m
3) B wins by 32 m
4) B wins by 100 m
5) A wins by 30 m
6) A wins by 60 m
7) B wins by 40 m
8) B wins by 60 m
9) Both reaches at same time
10) None of these

Solution

As A allows B a start of 160 m, so B covers (1600-160) = 1440 m and A covers 1600 m.
Given ratio of speeds of A and B = 10:9 => When B covers 9 m, A covers 10 m.
.'. when B covers 1440 m and complete the race, A covers (10/9)*1440=1600 m.
Therefore, both reaches post at the same time.
Correct option 9)

Correct Option: 9 Best Solution (1)

23 Feb 2022 Area

A cyclist starts with a constant speed of 20 km/h from a corner of a rectangular park and he completes one round along the boundary in 24 minutes. Find the area (in Km²) of a park, if the ratio between the length and the breadth of a park is 5:3.

OPtion

1) 1.875
2) 4.75
3) 2.25
4) 5.75
5) 4.25
6) 7.50
7) 3.75
8) 4.50
9) 3.25
10) None of these

Solution

Distance covered by cyclist for 1 complete round = 20*24/60 = 8 km = Perimeter of a park
Let the length and breadth of a park be 5x and 3x respectively, then Perimeter = 2(5x+3x) = 16x
.'. 16x = 8 km => x=0.5
Therefore, Area of park = 5x*3x = 15x² = 15*0.5*0.5 = 3.75 km²

Correct Option: 7 Best Solution (2)

22 Feb 2022 Clocks and Calendars

A clock is set at 2 pm on 22 February 2022. If the clock gains 2 Minutes in 22 hours. What will be the right time (to nearest minute) when the clock indicates 2 pm on 2 March 2022 ?

OPtion

1) 1:55 pm
2) 2:17 pm
3) 2:06 pm
4) 1:33 pm
5) 1:37 pm
6) 1:43 pm
7) 1:40 pm
8) 1:13 pm
9) 1:52 pm
10) None of these

Solution

Time between 2 pm of 22 Feb and 2 pm of 2 Mar=8 days=192 hrs
Given, Clock gains 2 min in 22 hrs.
=> When Clock shows 22 hrs & 2 min or 22(2/60) hrs or 661/30 hrs, Actual time 22 hrs.
When Clock shows 192 hrs, Actual time = 192x22/(661/30) = 191.7095 hrs
= 191 hrs 42.57 min ~ Approx 17 min to 2 pm on 2 march
Hence, correct time is 1:43 pm.

Correct Option: 6 Best Solution (0)

21 Feb 2022 Profit & Loss

On purchase of 3 toys, a shopkeeper offers a discount of 10% on marked price and 1 toy free. Even then shopkeeper earns a profit of 20%, then the ratio of marked price to cost price is

OPtion

1) 14:9
2) 16:9
3) 10:7
4) 11:7
5) 8:5
6) 9:5
7) 4:3
8) 7:5
9) 5:2
10) None of these

Solution

On MP, of 3 toys, he is giving 10% discount and 1 toy free. Thus of selling 4 toys he is getting 20% profit.
=> 90% of MP of 3 toys = 120% of CP of 4 toys
(90/100)*3*MP = (120/100)*4*CP
=> MP/CP = 16/9

Correct Option: 2 Best Solution (3)