M4maths Previous Puzzles

18 Aug 2020 Numbers

The product of two numbers is 39375 and the quotient, when the larger one is divided by the smaller, is 7. The sum of the numbers is :

OPtion

1) 800
2) 500
3) 600
4) 840
5) 640
6) 540
7) 480
8) 700
9) 750
10) None of these

Solution

Let the numbers be x and y.
Then, xy = 39375 and x/y = 7.
(xyxy//)=39375/7
=>y2 =5625
=> y = 75
=> x = 7y = 7 x 75 = 525.
Sum of the numbers = 525 + 75 = 600.

Correct Option: 3 Best Solution (6)

17 Aug 2020 Numbers

Three numbers are in the ratio 3 : 6 : 9 and their average is 66. The largest number is :

OPtion

1) 72
2) 81
3) 90
4) 99
5) 60
6) 66
7) 100
8) 110
9) 144
10) None of these

Solution

Let the numbers be 3x, 6x and 9x, Then, (3x + 6x + 9x ) / 3 = 66

=> 6x = 66

=> x = 11.

Largest = 11x = 11*9 = 99

Correct Option: 4 Best Solution (4)

14 Aug 2020 Permutation

A five-digit number is formed using digits 1, 3, 5, 8 and 9 without repeating any one of them. What is the sum of all such possible numbers?

OPtion

1) 6666600
2) 6666680
3) 6606600
4) 6066600
5) 6931264
6) 6933264
7) 6932264
8) 6934264
9) 6935264
10) None of these

Solution

If we fix 1 at the unit’s place, the other digits can be arranged in 4! = 24 ways.

So, there are 24 numbers which have 1 at the unit’s place and sum of these numbers is 24.

Similarly, there will be 24 numbers each with 3, 5, 8 and 9 at the unit’s place.

So, the sum of all the numbers at the unit’s place will be:

24 + 24 × 3 + 24 × 5 + 24 × 8 + 24 × 9 = 624

Similarly, the sum of the digits at the ten’s place, hundred’s place,

thousand’s place and ten thousand’s place will be 624.

So, the sum of all numbers = 624 (1 + 10 +100 +1,000 +10,000) = 6933264

Correct Option: 6 Best Solution (5)

13 Aug 2020 Race

In a mile race, Yuvraj can be given a start of 128 m by Virat. If Virat can give Rohit a start of 4 m in a 100 m dash, then who out of Yuvraj and Rohit will win a race of one and half miles, and what will be the final lead given by the winner to the loser? One mile is 1,600 m.

OPtion

1) Yuvraj, 10 m
2) Rohit, 10 m
3) Yuvraj, 25 m
4) Rohit, 25 m
5) Yuvraj, 50 m
6) Rohit, 50 m
7) Yuvraj, 80 m
8) Rohit, 80 m
9) Rohit, 100 m
10) None of these

Solution

In a mile race, Yuvraj can be given a start of 128 m by Virat. This means that Virat can afford to start after Yuvraj has traveled 128 m and still complete one mile with him. In other words, Virat can travel one mile, i.e. 1,600 m in the same time as Yuvraj can travel (1600 – 128) = 1,472 m. Hence, the ratio of the speeds of Virat and Yuvraj = Ratio of the distances traveled by them in the same time = 1600/1472 = 25 : 23.

Virat can give Rohit a start of 4 miles. This means that in the time Virat runs 100 m, Rohit only runs 96 m. So the ratio of the speeds of Virat and Rohit = 96 : 100 = 25 : 24.

Hence, we have B : A = 25 : 23 and B : C = 25 : 24. So A : B : C = 23 : 25 : 24. This means that in the time Rohit covers 24 m, Yuvraj only covers 23 m. In other words, Rohit is faster than Yuvraj. So if they race for 1.5 miles = 2,400 m, Rohit will complete the race first and by this time Yuvraj would only complete 2,300 m. In other words, Rohit would beat Yuvraj by 100 m

Correct Option: 9 Best Solution (1)

12 Aug 2020 Probability

A letter is randomly picked from the word:
INDEPENDENCE

What is the Probability that it would be a vowel?

OPtion

1) 1/2
2) 2/3
3) 5/11
4) 1/3
5) 5/12
6) 4/11
7) 5/13
8) 1/4
9) 1/3
10) None of these

Solution

Total letters in INDEPENDENCE = 12

Total Vowels =5
E=4
I=1

Probability = 5/12

Correct Option: 5 Best Solution (1)

11 Aug 2020 Simple Interest

At what rate percent per annum will a sum of money double in 6 years.

OPtion

1) 20%
2) 15%
3) 12.5%
4) 14%
5) 16%
6) 16.67%
7) 18%
8) 17.33%
9) 11.66%
10) None of these

Solution

Let principal = P, Then, S.I.= P and Time = 8 years



We know that S.I. = PTR/100



Rate = [(100 x P)/ (P x 6)]% = 12.5% per annum.

Correct Option: 6 Best Solution (3)

10 Aug 2020 Profit & Loss

Find the cost price of 1KG of Cashews which is sold for Rs. 690 at a loss of 8%.

OPtion

1) 800
2) 725
3) 750
4) 820
5) 850
6) 860
7) 720
8) 775
9) 700
10) None of these

Solution

If CP 100 SP 92
i.e. When SP 92, CP 100
when SP 690, CP = 100*690/92 = 750

Correct Option: 3 Best Solution (1)

07 Aug 2020 Permutation and Combination

In how many ways a team consisting of 5 boys and 3 girls, can be chosen from 9 boys and 12 girls.

OPtion

1) 27710
2) 27720
3) 27740
4) 27780
5) 27716
6) 27732
7) 27764
8) 27128
9) 27700
10) None of these

Solution

Choose 5 boys out of 9 boys = 9C5 ways = 126 ways

Choose 3 girls out of 12 girls = 12C3 ways = 220 ways

The committee can be chosen in = 126 * 220 = 27720 ways

Correct Option: 2 Best Solution (1)

06 Aug 2020 Race

In a 10 km race. Sushant, Rajkumar, and Suraj, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If Sushant beats Rajkumar by 1 km and Rajkumar beats Suraj by 1 km, then by how many metres does Sushant beat Suraj?

OPtion

1) 1.5 km
2) 1.6 km
3) 1.8 km
4) 1.9 m
5) 2.0 km
6) 2.1 km
7) 1900 km
8) 1800 m
9) 1900 m
10) None of these

Solution

Sushant : Rajkumar = 10 : 9
Rajkumar : Suraj = 10 : 9
⇒ The ratio of speeds of Sushant : Rajkumar : Suraj = 100 : 90 : 81
In the same time that Sushant travels 100 m, Suraj travels 81 metres ⇒ In the same time that Sushant travels 10000 m, Suraj would travel 8100 m
or Sushant would beat Suraj by 1900 m.

Correct Option: 9 Best Solution (5)

05 Aug 2020 Profit & Loss

A tea seller prepares and sells 150 tea cups every day. The total cost incurred on preparing 150 cups of team without any profit or loss is Rs 1275, he sells each cup of tea at Rs 10.

One day while preparing tea, unfortunately, 5 cups of tea get spilled while boiling.
How much is his profit or loss percentage for that day?

OPtion

1) Profit 13.17
2) Profit 12.75
3) Loss 13.73
4) Loss 12.75
5) Profit 13.13
6) Profit 13.87
7) Loss 13.13
8) Loss 13.87
9) Profit 13.73
10) None of these

Solution

CP of 150 Cups = 1275
SP of 150 Cups = 1500
SP of 145 Cups of tea = 1450

Profit = 1450 - 1275 = Rs 175
Profit % = (175/1275) = ~13.73%

Correct Option: 9 Best Solution (0)