M4maths Previous Puzzles

13 Oct 2020 Speed

Fatafat express train traveling at 90 kmph crosses a platform in 30 seconds and a person standing on the platform in 18 seconds. What is the length of the platform in meters?

OPtion

1) 400
2) 350
3) 200
4) 300
5) 250
6) 275
7) 280
8) 325
9) 390
10) None of these

Solution

Length of the platform = speed of train * extra time taken to cross the platform.
Length of platform = 90 kmph * 12 seconds

Convert 90 kmph into m/sec
1 kmph = 5/18 m/s
∴ 72 kmph = 5/18∗90 = 25 m/sec

Therefore, length of the platform = 25 m/s * 12 sec = 300 meters.

Correct Option: 4 Best Solution (0)

12 Oct 2020 Profit & Loss

Find the cost price of 1KG of Lotus seeds which is sold for Rs. 819 at a loss of 9%.

OPtion

1) 780
2) 770
3) 860
4) 800
5) 909
6) 1000
7) 900
8) 1100
9) 880
10) None of these

Solution

If CP 100 SP 91
i.e. When SP 91, CP 100
when SP 819, CP = 100*819/91 = 900

Correct Option: 7 Best Solution (0)

09 Oct 2020 Find the value of

If
6x - 4y = 8
8x = 5y + 13
Then what is the value of 6x -3y?

OPtion

1) 18
2) 21
3) 12
4) 16
5) 15
6) 6
7) 8
8) 9
9) 10
10) None of these

Solution

6x - 4y = 8 ---- (i)
8x - 5y = 13 ---- (ii)

Subtracting (i) from (ii), we get: 2x - y = 5
Multiplying both sides by 3 we get 6x -3y = 15

Option 3)

Correct Option: 5 Best Solution (1)

08 Oct 2020 Work and Time

Rohit and Virat, working together, can complete an assigned task in 20 days. If Rohit worked alone and completes half the task and then Virat takes over and completes the remaining half, then the task gets completed in 45 days. How long will Rohit take to complete the task if he worked alone? Assume that Rohit is more efficient than Virat.

OPtion

1) 25
2) 20
3) 35
4) 36
5) 18
6) 30
7) 45
8) 50
9) 60
10) None of these

Solution

Let Rohit take 'x' days to complete the task if he worked alone.

Let Virat take 'y' days to complete the task if she worked alone.

Given that They will complete the task in 20 days, if they worked together.

In 1 day, Rohit will complete 1/x of the task.

In 1 day, Virat will complete 1/y of the task.

Together, in 1 day they will complete 120 of the task.

Therefore,1/x + 1/y = 1/20 .... (1)


As per question if Rohit worked alone and completed half the work and then Virat takes over and completes the second half, the task will be completed in 45 days.

Rohit will complete half the task in x/2 days.

Virat will complete half the task in y/2 days.

∴ x/2 + y/2 = 45

Or, x + y = 90 or x = 90 - y .... (2)


Solving 1 and 2 we get
y^2 - 90y + 1800 = 0

=> y 30 or 60
The question clearly states that Rohit is more efficient than Virat. Therefore, Rohit will take lesser time than Virat.
So Rohit will take 30 days

Correct Option: 6 Best Solution (0)

07 Oct 2020 Handshakes

In a party there are 123 persons present. If each of them shakes hand with all the other persons,in total how many handshakes will take place?

OPtion

1) 7503
2) 7513
3) 7523
4) 7533
5) 7543
6) 7553
7) 7563
8) 7573
9) 7583
10) None of these

Solution

Out of 123 persons, the first person will shake hand with 122 persons.
The second person will shake hand with 121 persons (because he has already shaken hand with first person).
The third person will shake hand with 120 persons and so on. The second last person shakes hand with only one person. And last will shake hand with none
(because he has already shaken hand with all persons).
In order to find the total number of handshakes you have to add all the natural numbers from 1 to 122 i.e. ∑ 122.
∑122 = 123 x 122/2 = = 7503 handshakes.

Correct Option: 1 Best Solution (2)

06 Oct 2020 Profit and Loss

The profit earned by selling a chocolate for Rs 900 is double the loss incurred when the same chocolate is sold for Rs.490. At what price should the chocolate be sold to make 25% profit?

OPtion

1) 720
2) 750
3) 700
4) 775
5) 780
6) 790
7) 800
8) 820
9) 725
10) None of these

Solution

Let C.P be Rs. x

900 - x = 2(x - 490) => x = Rs.626.67



C.P = 626.67 gain required is 25%

S.P = [(100+25) x 626.67] / 100 = Rs.783.33

Correct Option: 10 Best Solution (0)

05 Oct 2020 Average

The average of runs scored by Afridi of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?

OPtion

1) 71
2) 69
3) 73
4) 67
5) 75
6) 76
7) 66
8) 65
9) 64
10) None of these

Solution

Average = total runs / no.of innings = 32

So, total = Average x no.of innings = 32 x 10 = 320.



Now increase in avg = 4runs. So, new avg = 32+4 = 36runs

Total runs = new avg x new no. of innings = 36 x 11 = 396

Runs made in the 11th inning = 396 - 320 = 76

Correct Option: 6 Best Solution (1)

02 Oct 2020 RANK of the word

Rank of the word GANDHI in the dictionary of words formed by the letters of the word GANDHI?

OPtion

1) 209
2) 249
3) 258
4) 257
5) 255
6) 259
7) 253
8) 251
9) 250
10) None of these

Solution

240 + 0 + 18 + 0 + 0 + 0 = 258
258 + 1 = 259
i.e., Rank of the word 'GANDHI' = 259

Correct Option: 6 Best Solution (3)

01 Oct 2020 Find the value of

If 49a^2 + 30ab + 25b^2 - 100ab = 289
then what is the value of (2187)^a/(243)^b = ?

OPtion

1) 903981141
2) 387420489
3) 043046721
4) 129140163
5) 903961141
6) 387460489
7) 043049721
8) 129180163
9) 387120489
10) None of these

Solution

49a^2 + 30ab + 25b^2 - 100ab = 289
=> 49a^2 -70ab +25b^2 =289
=> (7a-5b) ^ 2 = 289
=> 7a - 5b = 17

2187^a/243^b = 3^(7a) / 3^(5b) = 3^(7a-5b)
Now, 7a - 5b = 17

=> so 3^(7a-5b) = 3^17 = 129140163
Option 4)

Correct Option: 4 Best Solution (1)

30 Sep 2020 Arithmetic

A page is torn from a book. The sum of the remaining digits is 1097. What are the page numbers on page torn from this book?

OPtion

1) 17, 18
2) 18, 19
3) 10, 11
4) 11, 12
5) 13, 14
6) 12, 13
7) 19, 20
8) 14, 15
9) 15, 16
10) None of these

Solution

Let the total pages are 'n'. We have
1 + 2 + 3 + .........+n = 1097
⇒ n(n+1)/2 = 1096
n (n+1) = 2194
The square nearest to 2194 is 2209.This is the square of 47. Hence, we will take n= 63.
Therefore, sum of the pages= n(n+1)/2 = 47*48/2= 1128
Missing number = 1128-1097 =31.
Now, we have to think of 2 consecutive numbers whose sum is 31.
x+x+1=31 ⇒ ×= 15, x+1= 16

Correct Option: 9 Best Solution (0)