M4maths Previous Puzzles

25 Mar 2022 Time and Work

A and B together can finish a work at their usual efficiencies in 36 days. If A had worked at 2/3 of his usual efficiently and B had worked at twice his usual efficiently, then the work would have been completed in 30 days. How many days would A take to finish the task if he works alone at twice the usual efficiency?

OPtion

1) 90
2) 45
3) 24
4) 20
5) 72
6) 30
7) 15
8) 60
9) 36
10) None of these

Solution

Let A and B can do A unit and B unit of work per day respectively, then 36A + 36B = 1 ----(i)
Now, with A working with 2/3 efficiently and B with twice efficiency, it takes 30 days to finish => 30*(2/3)*A + 30*2B = 1
20A + 60B = 1 ----(ii)
Solving (i) & (ii), we get, A=1/60, B=1/90
When A works alone with twice effeciency, his 1 day work = 2*A = 2*1/60 = 1/30
.'. A would finish the work in 30 days.

Correct Option: 6 Best Solution (2)

24 Mar 2022 Alligation and Mixture

Liquids A and B are mixed in the ratio 5:3 and the mixture is sold at Rs. 42 with a profit of 20%. If the liquid A costs Rs 4 more than the liquid B, then the cost price of liquid A (in Rs) is

OPtion

1) 35
2) 36
3) 40
4) 33.5
5) 37.5
6) 35.5
7) 32.5
8) 36.5
9) 34.5
10) None of these

Solution

The mixture is sold at 20% profit for Rs. 42 /Liter, .'. CP of mixture = (100/120)*42 = Rs. 35 /Liter
Let CP per liter of liquid A = Rs. x and liquid B =Rs. (x-4)
Given, ratio of liquid A & B = 5:3
In 8 liter mixture, liquid A= 5 liters and Liquid B=3 Liters
Then, CP of 8 liter mixture = [5x + 3(x-4)] / 8 = 35
8x - 12 = 280
x = 36.5 Rs.
Correct Option 8)

Correct Option: 8 Best Solution (3)

23 Mar 2022 Area and Volume

A cuboid with sides in the ratio 8:5:6 is cut perpendicular to its length to form three smaller cuboids of equal size. If sum of the surface areas of all three cuboids is 1080 cm² more than the surface area of original cuboid, then the volume of original cuboid (in cm³) is

OPtion

1) 4320
2) 5280
3) 6480
4) 6720
5) 6240
6) 7200
7) 6960
8) 5760
9) 7440
10) None of these

Solution

Let length, breadth & height of original cuboid be L, B, H respectively.
Then, its Curved Surface Area = 2(LB + BH + LH) -----(i)
Dimension of each new cuboid are L/3, B, H (Breadth and height being same)
Curved Surface Area of 3 new cuboids = 3*2[(L/3)B + BH + (L/3)H] = 2LB + 6BH + 2LH ---(ii)
Difference of Curved Surface Area (ii) - (i) = 4BH = 1080
BH = 270
Let Length, Breadth & Height of original cuboid be 8x, 5x, 6x respectively, then 5x*6x = 270
30x² = 270 or x = 3
So, sides of original cuboid are L=24 cm, B=15 cm, H=18 cm
.'. Volume of original cuboid = L*B*H = 24*15*18 = 6480 cm³.
Correct option 3)

Correct Option: 3 Best Solution (2)

22 Mar 2022 Profit & Loss

Ramesh purchased a mobile phone for Rs. 15,000. He sold it to Suresh at a gain of 20% of the selling price. Suresh further sold it to Mahesh for Rs. 20,000. What was the profit percentage of Suresh ?

OPtion

1) 16.66
2) 11.11
3) 66.66
4) 8.88
5) 6.66
6) 5.55
7) 33.33
8) 9.99
9) 22.22
10) None of these

Solution

Here, Ramesh sold mobile phone to Suresh at a gain of 20% on SP
SP = CP + Profit
SP = CP + 0.2*SP
0.8*SP = 15000
SP = 18750 = CP of Suresh
.'. Profit of Suresh = 20000 - 18750 = 1250 Rs.
% Profit = (1250/18750)*100 = 6.66 %

Correct Option: 5 Best Solution (2)

21 Mar 2022 Alligation and Mixture

A food contains 550 grams of a mixture of two foods varieties, X and Y. Food X contains 20% carbohydrate and food Y contains 35% carbohydrate. If this diet provides exactly 140 grams of carbohydrate, then how many grams of food X are in the mixture ?

OPtion

1) 385
2) 335
3) 380
4) 400
5) 345
6) 285
7) 330
8) 350
9) 325
10) None of these

Solution

Let x be the number of grams of Food X in the mixture, then number of grams of food Y=(550-x)
Total carbohydrate = Carbohydrate from Food X + Carbohydrate from Food Y
140 = 0.2x + 0.35(550-x)
52.5 = 0.15x
x = 350

Correct Option: 8 Best Solution (1)

18 Mar 2022 Percentage

For purchasing colours for Holi, Neel and Rajat went to market where colours were available in sachets. Neel purchased 5 Green, 3 Red and 9 Yellow coloured sachet and used up all his money while Rajat purchased 6 Green, 6 Red, and 18 Yellow coloured sachets and paid 60% more than what Neel paid. What percentage of the Neel's money was spent on purchasing Green colour ?

OPtion

1) 33.33
2) 66.66
3) 62.50
4) 37.50
5) 10
6) 30
7) 60
8) 50
9) 90
10) None of these

Solution

Let the total amount spent by Neel = x
Then, 5G + 3R + 9Y = x ----(i)
Also, spending of Rajat = 6G + 6R + 18Y = 1.6x ---(ii)
Multiplying Eqn (i) by 2, we get 10G + 6R + 18Y = 2x ---(iii)
Now subtracting Eqn (ii) from (iii), 4G=0.4x or G=0.1x
Neel's spending of Green colour 5G = 0.5x = 50% of x

Correct Option: 8 Best Solution (3)

17 Mar 2022 Coding & Decoding

In a certain code if BLUE is coded as 160, GREEN as 245, then how would YELLOW be coded?

OPtion

1) 525
2) 554
3) 492
4) 534
5) 558
6) 552
7) 545
8) 522
9) 498
10) None of these

Solution

When letters from A to Z are numbered from 1 to 26 respectively, the coded number is product of Sum of the numbers associated with letters and number of letters.
B L U E = (2 + 12 + 21 + 5) x 4 = 160
G R E E N = (7 + 18 + 5 + 5 + 14) x 5 = 245
Y E L L O W = (25 + 5 + 12 + 12 + 15 + 23) x 6 = 552

Correct Option: 6 Best Solution (2)

16 Mar 2022 Time Distance & Speed

A car leaves point A at 3:30 pm and moves towards point B at a uniform speed. A train leaves point B at 4:03 pm and moves towards point A at a uniform speed which is 5/4 that of the car. They meet at 5:15 pm at a point which is 161 km away from A. What is the distance between A and B?

OPtion

1) 273 km
2) 237 km
3) 299 km
4) 256 km
5) 286 km
6) 268 km
7) 301 km
8) 271.4 km
9) 249.32 km
10) None of these

Solution

Till they meet, car covers 161 km in 1 hrs 45 min or 7/4 hrs.
.'. Speed of a car = 161/(7/4) = 92 km/hr
Speed of train = (5/4)*92 = 115 km/hr
Time taken by train till they meet = 1 hr 12 min = 6/5 hrs
.'. Distance covered by train = Speed*Time = 115*6/5 = 138 km.
Total distance between A and B = Sum of the distances covered by car and train till they meet = 161+138 = 299 km.

Correct Option: 3 Best Solution (2)

15 Mar 2022 LCM & HCF

What is the LCM of 5/9, 2/15, 7/12, 4/21 ?

OPtion

1) 3/70
2) 14/3
3) 7/3
4) 3/35
5) 70/3
6) 7/30
7) 35/3
8) 140/3
9) 98/3
10) None of these

Solution

LCM (5/9, 2/15, 7/12, 4/21) = LCM (5, 2, 7, 4) / HCF (9, 15, 12, 21) = 140/3
Correct Option 8)

Correct Option: 8 Best Solution (3)

14 Mar 2022 Number System

In how many ways 9800 can be written as a product of two numbers ?

OPtion

1) 24
2) 16
3) 12
4) 18
5) 14
6) 36
7) 32
8) 26
9) 20
10) None of these

Solution

9800 = 2^3 x 5^2 x 7^2
If a number is represented as p^a x q^b x r^c
Then, number of factors = (a+1)(b+1)(c+1)
.'. Number of factors = (3+1)(2+1)(2+1) = 36
And product of two factors = 36/2 = 18
Hence in 18 ways 9800 can be written as a product of two numbers.

Correct Option: 4 Best Solution (1)