M4maths Previous Puzzles

13 May 2022 Profit & Loss

In a End of Season Sale, to clear stock a shopkeeper offers 50 items in price of 20 items but still there is no loss or gain in this transaction. What is his usual gain percentage when there is no sale ?

OPtion

1) 50
2) 66.66
3) 133.33
4) 150
5) 250
6) 100
7) 400
8) 300
9) 200
10) None of these

Solution

Given, shopkeeper sells 50 items in price of 20 items but there is no loss or gain.
⇒ CP of 50 items = SP of 20 items
Let CP of 1 item=1, so CP of 50 items=50=SP of 20 items
.'. SP of 1 item=50/20=2.5
% profit = [(2.5-1)/1]*100 = 150%
Correct Option 4)

Correct Option: 4 Best Solution (0)

12 May 2022 LCM & HCF

LCM of two numbers is 60 times their HCF. If sum of LCM and HCF is 549. If one number is 45, then other number is

OPtion

1) 96
2) 132
3) 181
4) 162
5) 180
6) 126
7) 108
8) 216
9) 144
10) None of these

Solution

Given, one number=45 and LCM=60HCF. Let other number=x
We know, product of LCM & HCF = Product of two numbers
LCM*HCF = 45x
60HCF*HCF = 56x ----(i)
Also, LCM + HCF = 549
60HCF + HCF = 549
61HCF = 549
⇒ HCF=9
Now substituting HCF=9 in Eqn (i), we get 60*9*9 = 45x
⇒ x=108

Correct Option: 7 Best Solution (3)

11 May 2022 Number System

If P is a three digit number where first digit is three times the last digit and no digit is repeated. How many P are possible which are divisible by 6 ?

OPtion

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

Solution

Given, 1st digit is 3 times the 3rd digit. .'. The 3-digit number can be of the form 3 _ 1 ; 6 _ 2 ; 9 _ 3
Now, for a number to be divisible by 6, it should be an even number divisible by 2 and 3 both.
.'. Only possible numbers will be even numbers of the form 6 _ 2
So, the numbers are 612, 642, 672, Total 3
Correct Option 2)

Correct Option: 2 Best Solution (1)

10 May 2022 Ratio & Proportion

An alloy contains magnesium, copper and zinc in the ratio 3 : 4 : 2 and another alloy contains copper, zinc and nickel in the ratio 4 : 5 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of copper per kg in new alloy will be:

OPtion

1) 175 gm
2) 225 gm
3) 125 gm
4) 319.44 gm
5) 388.88 gm
6) 416.66 gm
7) 166.66 gm
8) 305.55 gm
9) 527.77 gm
10) None of these

Solution

In 1st alloy: Ratio of magnesium, copper, Zinc = 3 : 4 : 2
In 2nd alloy: Ratio of copper, zinc, nickel = 4 : 5 : 3
Now, let the weight of first alloy be 36 kg (taken as Magnesium=12 kg, Copper=16 kg, Zinc=8 kg) and
Weight of second alloy = 36 kg (taken as Copper=12 kg, Zinc=15 kg, Nickel=9 kg)
When two alloys are mixed in equal weights, total weight of third alloy=36+36=72 kg
Weights in 3rd alloy: Magnesium=12 kg, Copper=(16+12) kg, Zinc=(8+15) kg, Nickel=9 kg.
Weight of Copper in 3rd alloy = 28 kg per 72 kg
.'. Weight per kg = 28/72 kg = 388.88 gm..

Correct Option: 5 Best Solution (2)

09 May 2022 Pipes & Cisterns

A leak in the bottom of a tank can empty it in 8 hours. An inlet pipe fills the tank at the rate of 6 liters per minute. When the tank is full, the inlet is opened but leak emptied the tank in 9 hours. The capacity of the tank (in liters) is

OPtion

1) 25290
2) 24920
3) 29160
4) 24290
5) 25920
6) 29610
7) 29160
8) 21600
9) 24300
10) None of these

Solution

Let the capacity of tank = x liters
Tank emptied per hour by leakage = x/8
Tank filled per hour by inlet pipe = 6*60 = 360 litres
Effective filling per hour with inlet pipe & leakage = 360 - x/8
From the given data, in 9 hrs, full tank get emptied with inlet and leakage
.'. x + 9*(360 - x/8) = 0
(9/8)*x - x = 3240
x = 25920
Correct Option 5)

Correct Option: 5 Best Solution (1)

06 May 2022 Ratio & Proportion

Three professionals Alok, Bhuvan and Chaitanya have incomes from various sources in the ratio 9 : 6 : 7 and their expenses are in the ratio 15 : 9 : 8. If Alok could save 25% of his income, then the ratio of savings of Alok, Bhuvan and Chaitanya is

OPtion

1) 44 : 68 : 39
2) 45 : 68 : 39
3) 36 : 39 : 68
4) 45 : 38 : 68
5) 36 : 68 : 39
6) 46 : 38 : 69
7) 45 : 39 : 68
8) 44 : 40 : 69
9) 45 : 68 : 69
10) None of these

Solution

Let incomes of Alok, Bhuvan and Chaitanya be 9x, 6x and 7x respectively
And their expenditures be 15y, 9y and 8y respectively.
Then, savings of Alok = Income - Expenditure = 9x - 15y = 25% of 9x
⇒ 9x - 15y = (1/4)*9x
36x - 60y = 9x
27x = 60y or y = (9/20)*x
Similarly, savings of Bhuvan = 6x - 9y = 6x - 9*(9/20)*x = (39/20)*x
Savings of Chaitanya = 7x - 8y = 7x - 8*(9/20)*x = (68/20)*x
,', Required ratio of savings = (9/4)*x : (39/20)*x : (68/20)*x = 45 : 39 : 68

Correct Option: 7 Best Solution (1)

05 May 2022 Percentage

For a company, this year the price of raw material is reduced by 24% and a company purchased 240 kg more but the total expenditure on raw material is decreased by 18% as compared to previous year. The current requirement of raw material (in kg) is

OPtion

1) 3040
2) 3820
3) 3280
4) 4820
5) 5560
6) 4280
7) 5320
8) 3400
9) 5280
10) None of these

Solution

Let last year price=100 and required raw material= x kg, so expenditure=100x
This year, price=(100-24)=76 and requirement=(x+240) kg, so expenditure=76(x+240)
Current year expenditure = (100-18)% or 82% expenditure of previous year
76(x+240) = (82/100)*100x
38(x+240) = 41x
3x = 9120
x = 3040
.'. Current requirement = 3040 + 240 = 3280 Kg.
Correct Option 3)

Correct Option: 3 Best Solution (0)

04 May 2022 Probability

A box contains 4 blue, 3 red, 5 green and 6 yellow marbles. If three marbles are drawn at random, what is the probability that at least one is green?

OPtion

1) 32/51
2) 143/408
3) 65/102
4) 265/408
5) 65/136
6) 65/408
7) 27/272
8) 5/408
9) 5/18
10) None of these

Solution

Blue=4, Red=3, Green=5, Yellow=6, Total=18
Number of ways of drawing 3 balls out of 18 = 18C3 = 816
Ways of selecting no marble Green = (18-5)C3 = 13C3 = 286
Probability of no marble selected is Green = 286/816
So, probability of selecting at least 1 Green = 1 - Probability of selecting no Green = 1 - (286/816) = 530/816 = 265/408

Alternate Solution:
Probability of at least 1 green out of 3 drawn = (1 Green & 2 Non Green) Or (2 Green & 1 Non Green) Or All 3 Green
= (5C1x13C2 + 5C2x13C1 + 5C3) / 18C3
= (390+130+10) / 816
= 530/816
= 265/408

Correct Option: 4 Best Solution (2)

03 May 2022 Ratio & Proportion

There are 96 boys and 84 girls in a class. If 60% of the total students leave the class and 'n' number of girls joined again and the ratio of boys to girls become 4:5. Which of the following CAN NOT be the value of 'n' ?

OPtion

1) 45
2) 27
3) 81
4) 63
5) 72
6) 36
7) 42
8) 18
9) 54
10) None of these

Solution

Total number of students = 96+84 = 180
Number of students left = 60% of 180 = 108
Let in 108 students who left, there are x boys and (108-x) girls
After joining of n girls, new ratio of boys and girls = (96 - x) / [84 - (108-x) + n] = 4/5
4n = 576 - 9x
n = 144 - (9/4)x
Now, x (multiple of 4) can have the values from 24 to 60 to get +ve integer value of n and number of girls left (108-x) is less than 84.
For x=24, n=90
For x=28, n=81
.
.
For x=60, n=9
We observe that values of 'n' is multiple of 9 upto 90.
So, from the given options 42 can not be the value of 'n'

Correct Option: 7 Best Solution (2)

02 May 2022 Percentage

There are 501 million workers in organised and unorganised sectors in India. The ratio of female and male employee is 1:3 and skilled male employees are 51/5 times that of unskilled female employees. If 15% male employees are unskilled, then number of skilled female employees is

OPtion

1) 56,362,500
2) 125,250,000
3) 31,312,500
4) 281,812,500
5) 140,906,250
6) 187,875,000
7) 93,937,500
8) 62,625,000
9) 112,725,000
10) None of these

Solution

The ratio of female and male employee = 1:3 ⇒ % of female employees=(1/4)x100)=25% .'. Male employees=75%,
Unskilled male=15% ⇒ Skilled male=85%
Number of skilled male employees = 85% of 75% of Total employees = (85/100)*(75/100)*501 = 319.3875 million
Given, Skliled male = (51/5)*Unskilled female
319.3875 = (51/5)*Unskilled female
.'. Unskilled female = 31.3125 million
Skilled female = Total female - Unskilled female = 25% of 501 - 31.3125 = 93.9375 million = 93937500
Correct Option 7)

Correct Option: 7 Best Solution (1)