M4maths Previous Puzzles

18 Mar 2022 Percentage

For purchasing colours for Holi, Neel and Rajat went to market where colours were available in sachets. Neel purchased 5 Green, 3 Red and 9 Yellow coloured sachet and used up all his money while Rajat purchased 6 Green, 6 Red, and 18 Yellow coloured sachets and paid 60% more than what Neel paid. What percentage of the Neel's money was spent on purchasing Green colour ?

OPtion

1) 33.33
2) 66.66
3) 62.50
4) 37.50
5) 10
6) 30
7) 60
8) 50
9) 90
10) None of these

Solution

Let the total amount spent by Neel = x
Then, 5G + 3R + 9Y = x ----(i)
Also, spending of Rajat = 6G + 6R + 18Y = 1.6x ---(ii)
Multiplying Eqn (i) by 2, we get 10G + 6R + 18Y = 2x ---(iii)
Now subtracting Eqn (ii) from (iii), 4G=0.4x or G=0.1x
Neel's spending of Green colour 5G = 0.5x = 50% of x

Correct Option: 8 Best Solution (3)

17 Mar 2022 Coding & Decoding

In a certain code if BLUE is coded as 160, GREEN as 245, then how would YELLOW be coded?

OPtion

1) 525
2) 554
3) 492
4) 534
5) 558
6) 552
7) 545
8) 522
9) 498
10) None of these

Solution

When letters from A to Z are numbered from 1 to 26 respectively, the coded number is product of Sum of the numbers associated with letters and number of letters.
B L U E = (2 + 12 + 21 + 5) x 4 = 160
G R E E N = (7 + 18 + 5 + 5 + 14) x 5 = 245
Y E L L O W = (25 + 5 + 12 + 12 + 15 + 23) x 6 = 552

Correct Option: 6 Best Solution (2)

16 Mar 2022 Time Distance & Speed

A car leaves point A at 3:30 pm and moves towards point B at a uniform speed. A train leaves point B at 4:03 pm and moves towards point A at a uniform speed which is 5/4 that of the car. They meet at 5:15 pm at a point which is 161 km away from A. What is the distance between A and B?

OPtion

1) 273 km
2) 237 km
3) 299 km
4) 256 km
5) 286 km
6) 268 km
7) 301 km
8) 271.4 km
9) 249.32 km
10) None of these

Solution

Till they meet, car covers 161 km in 1 hrs 45 min or 7/4 hrs.
.'. Speed of a car = 161/(7/4) = 92 km/hr
Speed of train = (5/4)*92 = 115 km/hr
Time taken by train till they meet = 1 hr 12 min = 6/5 hrs
.'. Distance covered by train = Speed*Time = 115*6/5 = 138 km.
Total distance between A and B = Sum of the distances covered by car and train till they meet = 161+138 = 299 km.

Correct Option: 3 Best Solution (2)

15 Mar 2022 LCM & HCF

What is the LCM of 5/9, 2/15, 7/12, 4/21 ?

OPtion

1) 3/70
2) 14/3
3) 7/3
4) 3/35
5) 70/3
6) 7/30
7) 35/3
8) 140/3
9) 98/3
10) None of these

Solution

LCM (5/9, 2/15, 7/12, 4/21) = LCM (5, 2, 7, 4) / HCF (9, 15, 12, 21) = 140/3
Correct Option 8)

Correct Option: 8 Best Solution (3)

14 Mar 2022 Number System

In how many ways 9800 can be written as a product of two numbers ?

OPtion

1) 24
2) 16
3) 12
4) 18
5) 14
6) 36
7) 32
8) 26
9) 20
10) None of these

Solution

9800 = 2^3 x 5^2 x 7^2
If a number is represented as p^a x q^b x r^c
Then, number of factors = (a+1)(b+1)(c+1)
.'. Number of factors = (3+1)(2+1)(2+1) = 36
And product of two factors = 36/2 = 18
Hence in 18 ways 9800 can be written as a product of two numbers.

Correct Option: 4 Best Solution (1)

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)