M4maths Previous Puzzles

22 Apr 2022 Profit & Loss

A seller has two types of items in a store. He allows a discount of 15% on an item whose marked price is Rs. 480 and 25% on an item whose marked price is Rs. 720. If a customer paid total of Rs. 10824 and gets a total discount of Rs. 3096, then how many items of marked price Rs. 720 he has purchased ?

OPtion

1) 9
2) 8
3) 6
4) 7
5) 16
6) 14
7) 10
8) 15
9) 12
10) None of these

Solution

Let the customer purchased 'x' items of marked price 480 and 'y' items of marked price 720
Total Cost = 480x*0.85 + 720y*0.75 = 10824
⇒ 102x + 135y = 2706 ---(i)
Total Discount = 480x*0.15 + 720y*0.25 = 3096
⇒ 18x + 45y = 774 ---(ii)
Solving Eqn (i) & (ii), we get x=8, y=14
.'. Customer purchased 14 items of marked price Rs. 720

Correct Option: 6 Best Solution (1)

21 Apr 2022 Time and Work

B is more efficient than A and they together can complete a work in 18 days. Had A done 60% of the work and then B, the remaining work, then the work would have been completed in 39 days. B alone will complete 60% of the same work in

OPtion

1) 21 days
2) 24 days
3) 30 days
4) 27 days
5) 36 days
6) 45 days
7) 12 days
8) 18 days
9) 15 days
10) None of these

Solution

Let A and B alone takes 'a' and 'b' days respectively, then 1 day work of A & B = 1/a + 1/b = 1/18 ---(i)
When A does 60% or 3/5 work and B remaining 2/5 work, total days required = 39
⇒ (3/5)/(1/a) + (2/5)/(1/b) = 39 ---(ii)
Substituting 1/a=(1/18 - 1/b) from (i) into Eqn (ii), we get (3/5)/[(1/18 - 1/b)] + (2/5)/(1/b) = 39
54b/[5(b-18)] + 2b/5 = 39
54b + 2b(b-18) = 39*5(b-18)
2b² - 177b + 3510 = 0
2b² - 117b - 60b + 3510 = 0
b(2b - 117) - 30(2b - 117) = 0
(b - 30) (2b - 117) = 0
Considering +ve integer value of the days, b=30
⇒ B alone can complete the work in 30 days.
.'. For 60% of the work B require = (60/100)*30 = 18 days.

Correct Option: 8 Best Solution (0)

20 Apr 2022 Area and Volume

A rectangular tank is 20 m long and 21 m deep. If 10,000 liters of water is drawn off the tank, the level of the water in the tank goes down by 1.5 m. How many liters of water can a tank hold ?

OPtion

1) 1,12,000
2) 1,40,000
3) 1,26,000
4) 1,50,000
5) 98,000
6) 84,000
7) 14,000
8) 56,000
9) 70,000
10) None of these

Solution

1 m³ = 1000 litres
.'. 10,000 litres = 10 m³
Let the breadth of a tank = B meters, then volume of water in 1.5 m height = 20*1.5*B = 10 m³
30B=10 ⇒ B=1/3 m
Volume of a tank = L*B*H = 20*(1/3)*21 = 140 m³
Capacity in Litres = 140*1000 = 1,40,000
Option 2) is correct.

Correct Option: 2 Best Solution (1)

19 Apr 2022 Ratio & Proportion

If (a+b):c=11:9 and (b+c):a=5:3, then find a:b:c ​

OPtion

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

Solution

(a+b)/c = 11/9 ⇒ 9a + 9b = 11c ---(i)
(b+c)/a = 5/3 ⇒ 3b + 3c = 5a ---(ii)
Multiplying Eqn (ii) by 3, 9b + 9c = 15a ---(iii)
Now subtracting Eqn. (i) from (iii), we get 9c - 9a = 15a - 11c
20c = 24a or a/c = 5/6
As (a+b)/c = 11/9 ⇒ a/c + b/c = 11/9
5/6 + b/c = 11/9
⇒ b/c = 7/18
We have a:c = 5:6 and b:c = 7:18.
a : b : c = (5x3) : 7 : 18 = 15 : 7 : 18

Correct Option: 8 Best Solution (2)

18 Apr 2022 Time Distance & Speed

A man travels 840 km in 12 hours, partly by train and partly by car. If he had travelled all the way by train, he would have saved 1/4 of the time he would have taken to travel by car only and would have arrived at his destination 1 hour 30 minutes early. Find the distance he covered while travelling by car.

OPtion

1) 480 km
2) 380 km
3) 520 km
4) 540 km
5) 420 km
6) 360 km
7) 600 km
8) 270 km
9) 300 km
10) None of these

Solution

Total Distance = 840 km.
Total Time taken by Train and Car = 12 Hours
By travelling all the distance by train, he would have reached 1.5 hrs early i.e. He would have taken 12 - 1.5 = 10.5 hrs.
.'. Speed of the train = 840/10.5 = 80 kmph
Time taken by train to travel 840 km = (1 - 1/4)* Time taken by car to travel 840 km = 10.5
⇒ Time taken by car to travel 840 km = 10.5/(3/4) = 14 hrs
.'. Speed of car = 840/14 = 60 kmph
Let the distance covered by car = x km and by train = (840-x) km
Then, x/60 + (840-x)/80 = 12
Solving, we get x=360 km

Correct Option: 6 Best Solution (1)

15 Apr 2022 Permutation & Combination

Find the number of ways to arrange the letters of the word ' GOODFRIDAY ' if letters ' DAY ' are always together.

OPtion

1) 1814400
2) 151200
3) 907200
4) 241920
5) 120960
6) 15120
7) 60480
8) 30240
9) 45360
10) None of these

Solution

The word GOODFRIDAY has 10 different letters
When the letters DAY are kept together they can be supposed to form one letter.
Then we have to arrange letters GOODFRI (DAY)
Now 8 letters (7+1) can be arranged in 8!/2! (O being repeated twice)
The letters DAY can be arranged among themselves in 3! ways.
.'. Required number of ways = (8!/2!)*3! = 120960

Correct Option: 5 Best Solution (1)

14 Apr 2022 Ratio and Proportion

Two numbers are such that their difference, their sum and their product are in the ratio 1:5:24. The product of these two numbers is

OPtion

1) 60
2) 72
3) 48
4) 84
5) 96
6) 64
7) 144
8) 108
9) 120
10) None of these

Solution

Let the numbers be x and y, then (x-y) : (x+y) : xy = 1 : 5 : 24
(x-y)/(x+y)=1/5 ⇒ 2x=3y ---(i)
(x+y)/xy=5/24 ⇒ 24x + 24y = 5xy ----(ii)
On solving Eqn. (i) & (ii), we get x=12, y=8
.'. Required product x*y = 12*8 = 96

Correct Option: 5 Best Solution (2)

13 Apr 2022 Probability

A packet contains some blue, red and green pens such that the probability of picking a blue pen is 2/9 and probability of picking a green pen is 4/9. If number of red pens is 15 and if all the pens are numbered starting from 1, 2, 3, ... and so on, then what is the probability of getting one pen numbered as multiple of 7 or 11 ?

OPtion

1) 8/15
2) 4/15
3) 4/9
4) 1/5
5) 2/9
6) 7/20
7) 5/9
8) 1/3
9) 2/5
10) None of these

Solution

Given, P(Blue)=2/9, P(Green)=4/9 and number of red pens=15
As we know, P(Blue) + P(Red) + P(Green) = 1
P(Red) = 1 - P(Blue) - P(Green) = 1 - (2/9) - 4/9 = 3/9 = 1/3
As number of red pens = 15 = 1/3 of total pens
.'. Total number of pens=15*3=45 ⇒ Pens are numbered from 1 to 45
Numbers that are multiple of 7 = 7, 14, 21, 28, 35, 42
And numbers that are multiple of 11 = 11, 22, 33, 44
So, favourable outcomes = 6+4 = 10
So, probability of getting pen of multiple 7 or 11 = 10/45 = 2/9

Correct Option: 5 Best Solution (2)

12 Apr 2022 Time Distance & Speed

Train A whose length is four-fifth of that of train B crosses it travelling in opposite direction in a time which is 4/7 th of the time taken by train A to cross it when travelling in same direction. Calculate the ratio of the speeds of train A and train B.

OPtion

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

Solution

Let lengths of trains B = x, then length of train A = (4/5)*x
Distance covered in each case =x + (4/5)*x = (9/5)*x
Let the speed of train A and train B be S1 and S2 respectively.
Relative speed in same direction = (S1-S2)
Relative speed in opposite direction = (S1+S2)
According to given condition, Time taken to cross train B in opposite direction = (4/7)*Time taken to cross train B in same direction
(9/5)*x / (S1 + S2) = (4/7)*[(9/5)*x / (S1 - S2)]
7(S1 - S2) = 4(S1 + S2)
3S1 = 11S2
S1/S2 = 11/3

Correct Option: 4 Best Solution (0)

11 Apr 2022 Number Series

Find next number in the series 24, 36, 38, 95, 98, ?

OPtion

1) 245
2) 298
3) 343
4) 380
5) 362
6) 284
7) 392
8) 352
9) 367
10) None of these

Solution

Alternate multiplication and addition series
24 x 1.5 = 36
36 + 2 = 38
38 x 2.5 = 95
95 + 3 = 98
98 x 3.5 = 343

Correct Option: 3 Best Solution (1)