M4maths Previous Puzzles

18 Feb 2022 Ratio and Proportion

The ratio of marks obtained by three students is 7:8:9 and sum of their marks is 360. If average of their percentage marks is 60, then the maximum marks for which the examination was conducted were

OPtion

1) 250
2) 350
3) 300
4) 400
5) 200
6) 450
7) 150
8) 500
9) 550
10) None of these

Solution

Given ratio of their marks as 7:8:9 and total marks=360
So, their individual marks are 105, 120, 135 respectively.
Let the maximum marks in each paper be 'x', then
Average of their percentages = [(105/x)*100 + (120/x)*100 + (135/x)*100)]/3 = 60
(100/3x)(360) = 60
x = 200

Correct Option: 5 Best Solution (3)

17 Feb 2022 Time Distance & Speed

City corporation recently started a cab service from certain terminal, which runs at a speed of 30 km/h at an interval of 20 minutes each. A woman coming towards terminal observes that she crosses the cab at an interval of 15 minutes. The speed of a woman (in km/h) is

OPtion

1) 10
2) 20
3) 15
4) 12
5) 24
6) 30
7) 18
8) 9
9) 8
10) None of these

Solution

Let the speed of a woman=x km/h, then relative speed=(x+30) km/h
Distance traveled by cab in 20 min = Distance covered by woman at speed of (x+30) in 15 min.
30*(20/60) = (x+30)*(15/60)
10 = (x+30)*(1/4)
x = 10 km/h

Correct Option: 1 Best Solution (2)

16 Feb 2022 Ratio and Proportion

There are white, pink and blue colored balls in a basket . The ratio of the number of blue, white and pink balls respectively is 8 : 11 : 7. If there are more than 15 pink colored balls, what is the minimum number of total balls in a basket ?

OPtion

1) 52
2) 104
3) 91
4) 78
5) 64
6) 88
7) 26
8) 90
9) 100
10) None of these

Solution

Ratio of blue, white and pink balls = 8 : 11 : 7
Let their numbers be 8x, 11x and 7x respectively
Number of pink balls can be 7, 14, 21, ....
Given, there are more than 15 pink balls. To get minimum number of total balls, considering minimum number of pink balls=21
So, 7x=21 or x=3
Hence, minimum number of total balls = 8x+11x+7x = 26x = 26*3 = 78

Correct Option: 4 Best Solution (3)

15 Feb 2022 Number System

If N = 9^21 + 1, what is the remainder when N is divided by 8?

OPtion

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

Solution

9^21 = (8+1)^21 will give remainder 1 when divided by 8
So, 9^21 + 1 will give 1+1 = 2 as remainder.

Correct Option: 5 Best Solution (0)

14 Feb 2022 Arithmetic

To celebrate valentine day, Pranay started saving money daily from 1st February. He was saving Rs. 14 more than what he saved on previous day. On 14th February from the sum so accumulated, he spent 14% on flowers and Rs. 1400 of the remaining on gifts and Rs. 418 was still left with him. How much money did he saved on 1st February ?

OPtion

1) Rs. 88
2) Rs. 90
3) Rs. 76
4) Rs, 56
5) Rs. 52
6) Rs. 60
7) Rs. 72
8) Rs. 46
9) Rs. 50
10) None of these

Solution

Let he saved Rs 'x' on 1st Feb, so from 1st Feb to 14th Feb for 14 days, he saved x, (x+14), (x+28), (x+42), ......
Sum of 14 terms = 14x+1274
Money left after spending 14% on flowers & Rs. 1400 on gifts = (14x+1274)(1 - 0.14) - 1400 = 418
14(x+91)*0.86 = 1818
x+91 = 150.99
x = 59.99 ~ 60

Correct Option: 6 Best Solution (3)

11 Feb 2022 Ratio & Proportion

In a hostel, there is food provision enough for 60 days for certain number of students. If after 12 days, 80 more students joins so the remaining food quantity can last only for next 36 days. How many students were there initially in a hostel ?

OPtion

1) 200
2) 480
3) 360
4) 420
5) 180
6) 400
7) 300
8) 240
9) 150
10) None of these

Solution

Let initially there are 'x' students and each student require 1 unit of food daily, then total food quantity available=60x units
Food consumed by 'x' students in 12 days=12x units and remaining quantity=60x-12x=48x units
Now total number of students=x+80
So, 48x / (x+80) = 36
=> x=240

Correct Option: 8 Best Solution (1)

10 Feb 2022 Sequence & Series

Find the next number of the series 2, 2, 4, 18, 136, ....

OPtion

1) 1080
2) 1360
3) 1215
4) 1090
5) 1485
6) 1350
7) 1620
8) 1390
9) 1260
10) None of these

Solution

Series is formed by multiplying and subtracting 2, 4, 6, .. to previous number.
2 x 2 - 2 = 2
2 x 4 - 4 = 4
4 x 6 - 6 = 18
18 x 8 - 8 = 136
136 x 10 - 10 = 1350

Correct Option: 6 Best Solution (1)

09 Feb 2022 Number System

Mr. Raj purchased new vehicle. When his friend Mr. Ratan enquired about its number, Mr. Raj replied that it is 4-digit number with all different digits in ascending order. The ratio of first two digits and last two digits is equal. Also fourth digit at unit place is three times the second digit at hundred place. Mr. Ratan was good at Mathematics, so he quickly replied that there are two such a four digit numbers. Find the difference of these two numbers.

OPtion

1) 1133
2) 3605
3) 1100
4) 3311
5) 2266
6) 1122
7) 2233
8) 6622
9) 3322
10) None of these

Solution

Given, 4th digit is three times the 2nd digit, so possible 4 digits can be _ 1 _ 3 ; _ 2 _ 6 ; _ 3 _ 9
To get numbers in ascending order formed by different digits and equal ratio of first two digits and last two digits, we cann't take '0' at first place.
So, possible numbers are only 1236 and 2369
Hence required difference = 2369 - 1236 = 1133

Correct Option: 1 Best Solution (3)

08 Feb 2022 Alligation and Mixture

A milk man sells milk after mixing water to it to such a level that ratio of water and milk becomes 9:41 in a mixture. If he sells at a mark-up rate of 12%, find his actual profit percentage.

OPtion

1) 30%
2) 40%
3) 33.33%
4) 37.50%
5) 36.10%
6) 42.50%
7) 28.24%
8) 36.58%
9) 22.50%
10) None of these

Solution

Given ratio of water & milk = 9:41 => in 50 Ltr mixture, Water=9 and Milk=41 Ltr.
.'. In 100 Ltr mixture, Water=18, Milk=82 Ltr.
Let the cost of 1 Ltr milk be Rs 1, then CP of 100 Ltr mixture with 82 Ltr milk=Rs. 82
With 12% mark-up, SP of mixture=Rs. 112
Hence, Profit Percentage = [(112 - 82)/82]*100 = 36.58%

Correct Option: 8 Best Solution (1)

07 Feb 2022 Time and Work

A starts working on a job and continues for 18 days and completes 40% of the work. Then, he employs B and together they work for 24 days and completed the work. What is the ratio of efficiencies of A and B ?

OPtion

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

Solution

Ratio of efficiency can also be calculated by comparing their 1 day work.
Let, the total work=100 units.
40% work by A in 18 days => A's 1 day work = 40/18 units
Remaining 60% of total work is done by both A and B in 24 days.
.'. (A+B)'s 1 day work = 60/24
Now B's 1 day work = (A+B)'s 1 day work - A's 1 day work = 60/24 - 40/18 = 5/18
So, the ratio of efficiencies of A nd B = 40/18 : 5/18 = 8 : 1

Correct Option: 8 Best Solution (1)