M4maths Previous Puzzles

23 Dec 2020 COMBINATION

A Company wishes to simultaneously promote two of its 6 department heads out of 6 to assistant managers. In how many ways these promotions can take place?

OPtion

1) 14
2) 12
3) 10
4) 11
5) 13
6) 15
7) 16
8) 9
9) 18
10) None of the above

Solution

: This is a problem of combination.
Hence, the promotions can be done in 6 C2
= 6×5 / 2 = 15 ways

Correct Option: 6 Best Solution (2)

22 Dec 2020 PROBABILITY

Tickets numbered 1 to 37 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 10?

OPtion

1) 10/37
2) 37/10
3) 13/37
4) 37/13
5) 11/37
6) 37/11
7) 12/37
8) 37/12
9) 4/37
10) None of the above

Solution

Here, S = {1, 2, 3, 4, ...., 36,37}.
Let E = event of getting a multiple of 4 or 10= {4,8,12,16,20,24,28,32,36,10, 30}.
P(E) = n(E)/n(S) = 11/37

Correct Option: 5 Best Solution (2)

21 Dec 2020 Speed

Jackson travels a distance of 100km in 5 hrs. How much faster in kilometer per hr, on an average, must he travel to make a journey in 5/3 hr less time?

OPtion

1) 5 km/hr
2) 10km/hr
3) 6 km/hr
4) 8 km/hr
5) 9 km/hr
6) 8.5 km/hr
7) 6 km/hr
8) 7 km/hr
9) 6.5 km/hr
10) None of the above

Solution

Time required = (5 hrs – 5/3 hrs)
=(5 hrs – 100 mints) = (5 hrs – 1hr 40 mints)
= 3 hrs 20 mints = 3 1/3 hrs
Required speed = (100*3/10) km/hr =30 km/hr
Original speed = (100/5)km/hr = 20 km/hr
Difference speed = required speed – original speed
=(30-20) =10km/hr

Correct Option: 2 Best Solution (2)

18 Dec 2020 Cost

The cost of a Book and a Notebook are 100 rupee and 40 rupee respectively. If a shopkeeper gives a discount of 10 % and 4 % in the two items respectively. Then total cost of 10 books and 4 notebooks is?

OPtion

1) 1093.8
2) 1044.0
3) 1113.6
4) 1102.4
5) 1053.6
6) 1084.6
7) 1012.4
8) 992.0
9) 1062.8
10) None of the above

Solution

Total cost of books after taking discount of 10 % = 100 * 10 * 0.9 = 900
Total cost of notebooks after taking discount of 4 % = 40 * 4 * .96 = 153.6
Hence total cost of 10 books and 4 notebooks is = 900+153.6 = 1053.6

Correct Option: 5 Best Solution (2)

17 Dec 2020 Permutation & Combination

How many words can be formed by using all the letters of the word JEWELLER, if W and J are respectively the first and last letters of the words formed?

OPtion

1) 24
2) 960
3) 96
4) 120
5) 720
6) 780
7) 60
8) 960
9) 1920
10) None of these

Solution

Since first and last letters are fixed so no. of methods to arrange other 6 letters = 6*5*4*3*2*1/3*2*1*2*1 = 60

Correct Option: 7 Best Solution (2)

16 Dec 2020 Age

The ratio of Satish’s age to Anil’s age is 5:1. The product of their ages is 180. What will be the ratio of their age after 5 years?

OPtion

1. 36:11
2. 40:11
3. 10:3
4. 12:3
5. 35:11
6. 42:11
7. 35:7
8. 32:5
9. 30:7
10. None of the above

Solution

Let the ages of Anil and Satish be x and 5x respectively.
Then as given, 5x X x = 180
Or 5x^2 = 180, x^2 = 180/5 =36
x = 6 years
So, Anil age is 6 years and Satish age is 30 years.
After 5 years Anil age will be 11 years and Satish age will be 35 years.
Hence the ratio of their age = 35 : 11

Correct Option: 5 Best Solution (2)

15 Dec 2020 Money

Find out the sum of money which produces ₹. 24630 interest in 4 years and 4 months at 3.5% p.a. simple interest?

OPtion

1. ₹ 150000
2. ₹ 160000
3. ₹ 162395.60
4. ₹ 165000
5. ₹ 164315.21
6. ₹ 158301.25
7. ₹ 165432.23
8. ₹ 148956.32
9. ₹ 155653.85
10. None of the above

Solution

We know I = P × it
i.e. 24630 = P x 3.5/100 × 52/12
24630 = (3.5/100 x P) × 13/3
24630 = (P x 45.5/300)
P = 24630×300/45.5
= ₹ 162395.60

Correct Option: 3 Best Solution (2)

14 Dec 2020 Age

The ratio of Satish’s age to Anil’s age is 5:1. The product of their ages is 180. What will be the ratio of their age after 5 years?

OPtion

1. 36:11
2. 40:11
3. 10:3
4. 12:3
5. 35:11
6. 42:11
7. 6:5
8. 8:3
9. 32:5
10. None of the above

Solution

Let the ages of Anil and Satish be x and 5x respectively.
Then as given, 5x X x = 180
Or 5x^2 = 180, x^2 = 180/5 =36
x = 6 years
So, Anil age is 6 years and Satish age is 30 years.
After 5 years Anil age will be 11 years and Satish age will be 35 years.
Hence the ratio of their age = 35 : 11

Correct Option: 5 Best Solution (4)

11 Dec 2020 Salary

A sum of amount of money is sufficient to pay Suraj’s salary for 24 days and Devesh’s salary for 42 days. The same money is adequate to pay the salary of both for.

OPtion

1) 12 days
2) 12.5 days
3) 13.2 days
4) 14 days
5) 15.27 days
6) 18 days
7) 18.27 days
8) 19.25 days
9) 14.56 days
10) None of the above

Solution

Let the total money be Rs.x
Suraj’s 1 day salary = Rs. x/24
Devesh’s 1 day salary = Rs. x/42
(Suraj + Devesh)’s 1 day salary = Rs(x/24+x/42)
= (4x+7x)/168 =11x/168
x = 168/11 = 15.27
Money is adequate to pay the salary of both for 15.27 days.

Correct Option: 5 Best Solution (3)

10 Dec 2020 Business

Vijay starts a business with Rs. 15500 and was joined afterwards by Bhuppi with Rs. 12000. When Bhuppi did joins if the profits at the end of the year were divided in the ratio 4:1?

OPtion

1) 4.2 months
2) 2.55 month
3) 3.56 month
4) 4.36 month
5) 5.62 month
6) 3.87 month
7) 2.98 month
8) 3.64 month
9) 4.25 month
10) None of the above

Solution

Let B joined the business for M months,
15500 x 12/ 12000 x M = 4/1,
12000 x M x 4 = 15500 x 12 x 1,
480M = 1860,
M = 1860/480 = 3.87 month

Correct Option: 6 Best Solution (3)