M4maths Previous Puzzles

11 Mar 2022 Probability

A bag contains 4 yellow, 5 red, 3 green, 4 black balls. If 4 balls are drawn randomly without replacement, what is the probability that the balls drawn contain balls of different colours?

OPtion

1) 2/91
2) 7/26
3) 12/91
4) 1/182
5) 6/91
6) 30/91
7) 5/182
8) 24/91
9) 11/26
10) None of these

Solution

Total balls = 4+5+3+4 = 16
Number of ways 4 balls can be drawn from 16 balls = 16C4
For the 4 balls to be of different colours, we need 1 ball each of yellow, red, green and black colour.
So favourable cases = 4C1 x 5C1 x 3C1 x 4C1
Required probability = 4C1 x 5C1 x 3C1 x 4C1 / 16C4 = 240/1820 = 12/91

Correct Option: 3 Best Solution (1)

10 Mar 2022 Boat and Streams

If the ratio of the speed of a boat in downstream and the speed of the stream is 10 : 1. If the boat can travel 320 km upstream in 20 hours then find the total distance travelled (in km) by the boat in still water in the same time?

OPtion

1) 320
2) 400
3) 420
4) 300
5) 360
6) 480
7) 520
8) 600
9) 720
10) None of these

Solution

Let the speed of boat in downstream = 10x km/hr and the speed of the stream = x km/hr
Upstream speed = 320/20 = 16 km/hr
Let the speed of boat in still water = b km/hr
Then, b - x = 16 ----(i)
Also, downstream speed = b + x = 10x => b = 9x
Substituting value of b in Eqn (i), we get 8x = 16 or x=2 km/hr.
From (i), Speed of the boat b = x + 16 = 18 km/hr
.'. Distance travelled by boat in 20 hours in still water = 20*b = 20*18 = 360 km.

Correct Option: 5 Best Solution (1)

09 Mar 2022 Number System

When 827 is added to 9A6, the result is 17B3. If 17B3 is divisible by 3, what is the largest possible value of A?

OPtion

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

Solution

8 2 7
+ 9 A 6
---------
1 7 B 3
There is 1 carry from sum of unit place and no carry from sum of hundred place.
For 17B3 to be divisible by 3, sum (1+7+B+3)=11+b should be divisible by 3.
Hence, B can be 1, 4, 7
As B cann't be less than 3. For B=4, A=1 and for B=7, A=4
.'. Largest value of A=4

Correct Option: 6 Best Solution (1)

08 Mar 2022 Time and Work

On 1st Feb 2022, Priya and Rakhi signed a contract of a work with a firm for Rs. 10,000 and started working immediately together for 8 hours per day. On 28th Feb 2022 they finished the work and the share of Priya was Rs. 1000 more than that of Rakhi. If Priya had worked alone for the same hours per day then on which date of the year 2022, she would have finished the work?

OPtion

1) 22nd March
2) 3rd April
3) 25th March
4) 6th April
5) 28th March
6) 4th April
7) 23rd March
8) 20th March
9) 24th March
10) None of these

Solution

Let the share of Priya=x and Rakhi=x-1000
So, x + (x-1000) = 10000
x = 5500
.'. Ratio of shares of Priya and Rakhi = 5500 : 4500 = 11 : 9
We know that share is directly proportional to efficiency
=> Priya completed 11/20 and Rakhi 9/20 of the total work in 28 days.
Hence, working alone Priya will take 28*20/11 = 50.9 days
Therefor, Priya alone can finish the work in 28 days of Feb + 22.9 days of March
So on 23rd March she will finish the work.

Correct Option: 7 Best Solution (3)

07 Mar 2022 Profit & Loss

A fruit-seller bought oranges at the rate of 6 for Rs. 20. How many oranges, he should sell in Rs. 820 in order to make a profit of 23% ?

OPtion

1) 266
2) 160
3) 320
4) 290
5) 180
6) 200
7) 360
8) 400
9) 233
10) None of these

Solution

CP of 1 orange = 20/6 = Rs. 10/3
Now SP of 1 orange with 23% profit = (10/3)*(123/100) = Rs. 41/10
.'. Number of oranges to be sold in Rs. 820 = 820/(41/10) = 200

Correct Option: 6 Best Solution (4)

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)