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Given :

A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%

Calculations :

Let the weight of box A be 100x 

Weight will be increased by 60% when the B box is placed on the top. 

So,

Weight of Box A + weight of box B = 100x + 60% of 100x 

100x + weight of box B = 160x 

Weight of box B = 60x 

Total weight of the box A and B = 100x + 60x 

⇒ 160x 

Now box B removed from the top 

So the per cent decrement in the weight = (60/160) × 100 

⇒ 37.5% 

∴ Option 4 is the correct choice. 

Given :

When a runner was crossing the 12 km mark, she was informed that she had completed only 80% of the race.

Calculations :

Let the total distance be 'x' km 

According to the question 

12 = 80% of x 

(4/5) of x = 12 

⇒ x = 15 km 

∴ Option 2 will be the correct choice.

Population in the beginning of the first year 

= 9975/[1+(5/100)]*[1-(5/100)] 

= [9975*(20/21)*(20/19)]

=10000

Given:

Each participant got points that are 2% of total number of participants

Each organizer got points that are 72% of the total number of organizers

Calculation:

Let participants be p

Let organizers be o

(2% of p) × p = (72% of o) × o

⇒ (p)²/(o)² = 72%/2%

⇒ (p)²/(o)² = 36

⇒ p/o = 6

⇒ p = 6 × o

We know that

⇒ 6 × o – o = 200

⇒ o = 40

⇒ p – o = 200

⇒ p = 240

Total number of points distributed

⇒ 2(2/100) × 240 × 240

⇒ 2304

∴ The total number of points distributed is 2304.

Amount of salt in 30 kg solution = [(20/100)*30]kg = 0.6 kg 

Let x kg of pure salt be added Then , 

(0.6+x)/(30+x)=10/100

60+100x=300+10x 

90x=240 

x=8/3.

Required Percentage = [((100/3)*100)/[100+(100/3)]]% 

=[(100/400)*100]%

=25%

Required percentage = [(20*100)/(100-20)]%=25%.

Given:

Monthly salary = Rs. 50,000

E = 60% of income

T = 20% of E

C = 15% of T

After salary got raised by 40%,

E = 60% of income

T = 30% of E

C = 20% of T

Calculations:

Let the initial salary be 1000x.

E = 60% of 1000x

⇒ 600x

T = 20% of 600x

⇒ 120x

C = 15% of 120x

⇒ 18x

Total expense = 600x + 120x + 18x

⇒ 738x

Initial savings = 1000x - 738x

⇒ 262x

After salary got raised by 40%,

New salary = 1000x + 1000x × 40%

⇒ 1400x

New E = 60% of 1400x

⇒ 840x

New T = 30% of 840x

⇒ 252x

New C = 20% of 252x

⇒ 50.4x

New Total expense = 840x + 252x + 50.4x

⇒ 1142.4x

New savings = 1400x - 1142.4x

⇒ 257.6x

Difference in savings = 262x - 257.6x

⇒ 4.4x

∵ 1000x = Rs. 50,000

⇒ x = 50

Difference in savings = 4.4x

⇒ 4.4 × 50

⇒ Rs. 220

∴ The difference between the two savings is Rs. 220.

Given:

Rahul gives 20% of some amount to his wife.

And, 20% of the remaining amount to charity

Remaining Amount = Rs. 12,800

Calculation:

Let be total amount of Rahul be 100 unit

Rahul gives his wife = 100 unit - 20 unit

⇒ Then remaining amount is 80 unit

Then he gives 20% in charity = 80 unit × 80%

⇒ Remaining amount is 64 unit 

Giving,

⇒ 64 unit = 12800

⇒ 1 unit = 200

⇒ Total monthly income = 200 × 100

∴ Rahul monthly income is 20,000.

Given:

Two numbers are less than the third number by 40% and 65% respectively.

Concepts used:

Percentage by which second number is less than first number = [(First number - second number)/First number × 100]

Calculation:

Let the third number be x.

First number = x – 40% of x

⇒ 60% of x = 0.60x

Second number = x – 65% of x

⇒ 35% of x = 0.35x

First number – Second number = 0.60x – 0.35x 

⇒ 0.25x

Percentage by which second number is less than first number = (First number – Second number)/First number] × 100

⇒ (0.25x/0.60x) × 100

⇒ 125/3 %

⇒ 41.67%

∴ Second number is less than the first number by 41.67%.

(i) 6% = 6/100 =0.06. 

(ii) 28% = 28/100 =0.28. 

(iii) 0.2% =0.2/100 = 0.002. 

(iv) 0.04%= 0.04/100 =0.004.

(i) 23/36 = [(23/36)*100]% = [575/9]% = 63 8/9%.

(ii) 6 3/4 =27/4 =[(27/4)*100]% = 675%. 

(iii) 0.004 = [(4/1000)*100]% = 0.4%.

Given:

Monthly savings of Ajay = ₹ 6400

Concept used:

Savings percentage  = (100 – Expense in percentage)/100

Calculation:

Let the monthly income be x

Expenses on rent = (36/100) × x

⇒ Remaining salary after expenses on rent = {(100 – 36)/100} × x

Expenses on bills = {64/100} × (40/100) × x

⇒ Remaining salary after expenses on bills = {64/100} × {(100 – 40)/100} × x 

Expenses on travelling = (2/3) × {64/100} × {60/100} × x 

⇒ Remaining salary after expenses on travelling = {(1 – 2)/3} × {64/100} × {60/100} × x 

⇒ Monthly savings in terms of x = {1/3} × {64/100} × {60/100} × x      ----(1)

Actual monthly savings = 6400      ----(2)

Equating equation (1) and (2)

⇒ (1/3) × (64/100) × (60/100) × x = 6400

⇒ x = 50000

∴ The monthly income of Ajay is ₹ 50000.

Given: Man Spent in house rent = 20% of income

Children education = 25% of remaining (after deduction of house rent)

Transportation = 10% of remaining (after deduction of house rent + transportation) = 1080

Let, Income of man = X

⇒ Expenditure in house rent = 20% of X = 0.2X

⇒ Balance left after house rent = X – 0.2X = 0.8X

⇒ Expenditure on children education = 25% of 0.8X = 0.2X

⇒ Balance left after children education = 0.8X – 0.2X = 0.6X

⇒ Expenditure on transportation = 10% of 0.6X = 0.06X

∴ 0.06X = 1080

∴ X = 1080/0.06 = 108000/6 = 18000

∴ 0.2X = 0.2 × 18000 = 3600

Therefore, expenditure on house rent = Rs. 3600

Shortcut Trick:

Let, Income of man = 100

Expenditure in house rent = 20, Balance left = 80

Expenditure on children education = 20, Balance left = 60

Expenditure on transportation = 6

∵ 6 = 1080

∴ 1 = 1080/6 = 180

∴ 100 = 18,000

GIVEN:

⇒ Per month savings = Rs. 24,000

ASSUMPTION:

⇒ Let total income = 100%

CALCULATION:

⇒ Rent paid = 20% of 100 = 20%

⇒ Remaining = 80%

⇒ EMI paid = 25% of Remaining = 20%

⇒ Remaining = 60%

⇒ Education = 20% of 60% = 12%

⇒ Remaining = 48%

⇒ 48% = Rs. 24,000

⇒ 1% = Rs. 500

Given:

Savings at the end of the month is Rs. 1300.

Formula used:

Percentage = (Part value/Original value) × 100

Calculation:

Person total percentage expenditure

\( \Rightarrow \;42_7^6\% \; + \;28_7^4\% \; + \;10\% \; = \;81_7^3\% \)

Percentage savings

\( \Rightarrow 100\; - \;81_7^3\% \; = \;18_7^4\% \)

Person total salary

\( \Rightarrow \;\frac{{1300 \times 7 \times 100}}{{130}}\)

⇒ 7000

∴ Person per month salary is Rs. 7000.

Given :

30% spends on groceries

20% of remaining spends on rent and

45% of the remaining spends on children's education

Calculation :

Let the total monthly income be Rs.100 units

⇒ groceries = 30 (now, remaining Rs.70)

⇒ rent = 20% of 70

⇒ rent = 14 units (now,remaining Rs. 70 - 14 = 56)

⇒ children's education = 45% of 56

⇒ children's education = 25.2

⇒Total spending = 30 + 14 + 25.2 = 69.2

⇒ Total monthly savings = 100 - 69.2

⇒ 30.8

according to question,

30.8 units = Rs.5544

⇒ 1 unit = Rs.180

∵ spending on rent is 14 units

∴ Arun spends Rs.2520 on rent

Given:

Man spends 75% of his income.

Income increases by 28% 

Expenditure increases by 20%

Concept:

Saving = Income – Expenditure 

Let the Income of a man = 100

Expenditure = 75% of 100

⇒ (75/100) × 100 = 75

Saving = Income – Expenditure 

Initial Saving = 100 – 75 = 25      ----(1)

Now as per the question,

His income increased by 28%

⇒ His new income = Old income + 28% of Old income

⇒ His new income = (128/100) × 100 = 128

Similarly, his expenditure increased by 20%

⇒ His new expenditure = (120/100) × 75

⇒ His new expenditure = 90

Saving_(new) = Income_(new) – Expenditure_(new)

⇒ Saving(new) = 128 - 90 = 38      ----(2)

Now, % increase in savings = {(38 – 25)/25} × 100      ----(from 1 and 2)

⇒ 13 × 4 = 52%

∴ The % increase in saving is 52%

Given:

Total monthly income of Virat = Rs. 24000

Total amount spent on rent every month = Rs. 5000

Total amount spent on food every month = Rs. 4000

Total amount spent on household items every month = Rs. 3000

The ratio of remaining amount divided between his savings and charity = 5 ∶ 1

Formula Used:

Savings = Income – Expenditure

The ratio of two numbers

Percentage of total amount spent on charity = (Amount spent on charity / Total amount spent) 

× 100

Calculation:

The remaining amount after spending on rent, food, and household items is obtained as:

24000 – (5000 + 4000 + 3000) = 12000

Hence, we can obtain the amount spent for charity every month as:

(1/6) × 12000 = 2000

We can obtain the percentage of the total amount he spends on charity as:

(2000/24000) × 100 = 8.33

∴ The percentage of the total amount he spends for charity every month is 8.33%

Given:

Percentage of total monthly income spent on rent = 20%

Percentage of total monthly income spent on food and travelling = 35%

Percentage of total monthly income spent on medical care = 15%

Monthly savings = Rs. 6000

Formula Used:

Total income spent = (Percentage of income spent/100) × total income

Expenditure = Income – Savings

Calculation:

Assume the monthly income = Rs. x

Hence, we obtain:

Monthly expenditure on Rent = (20/100) × x = 0.2x

Monthly expenditure on food and travelling = (35/100) × x = 0.35x

Monthly expenditure on medical care = (15/100) × x = 0.15x

Remaining amount, i.e. savings = x – (0.2x + 0.35x + 0.15x) = 0.3x

6000 = 0.3x

⇒ x = 6000/0.3

⇒ x = 20000

∴ Mandeep’s monthly income is Rs. 20000

Given:

Due to a reduction of 20% in the price of potato, Amit can purchase 6 kg more for Rs. 350.

Formula used:

Percentage = (value/total value) × 100

Calculation:

Due to 20% reduction in price Amit can Purchase 6 kg more

⇒ 20% = 6 kg

⇒ 100% = (6/20) × 100 = 30 kg

Now the total weight of Potato is 30 kg

Reduced price of 1 kg Potato = Rs. (350 / 30) = Rs. 11.67

Previous price of 1 kg Potato = Rs. (350 / 24) = Rs. 14.58

∴ Reduced and the previous price of 1 kg Potato are Rs. 11.67 and Rs. 14.58 respectively.

Shortcut Trick:

6 kg = 350

⇒ 1 kg = 350 / 6

Reduced price = Rs. {(350 / 6) × (20 / 100)} = Rs. 11.67

Previous price = Rs. {11.67 / (80 / 100)} = Rs. 14.58

∴ Reduced and the previous price of 1 kg Potato are Rs. 11.67 and Rs. 14.58 respectively.

Given:

The rise in the income of A is 20%.

He now spends Rs. 20,000 more which is double of the previous expenditure, keeping his savings same.

Formula Used:

Ratio of Profit = ratios of product of Amount invested and time

Income – savings = expenditure

Calculation:

Let initial income be Rs. 5x

New income be Rs. 6x

Let expenditure initially be Rs. y

New expenditure = Rs. (y + 20,000)

ATQ,

⇒ y + 20,000 = 2y

⇒ y = 20,000

Since savings is same

⇒ 5x – y = 6x – (y + 20,000)

⇒ 5x – 20,000 = 6x – y – 20,000

⇒ 5x – 20,000 = 6x – 40,000

⇒ x = 20,000

His increased income = 6x = Rs. (6 × 20,000) = Rs. 1,20,000

∴ His increased income is Rs. 1,20,000

Given:

A = 40% less than B

C = 50% of sum of A and B

Calculation:

Let the value of B be 100x

⇒ A = 100x × (60/100) = 60x

C = 50% of (60x + 100x)

⇒ 50% of 160x = 80x

Difference of A and B = 100x – 60x = 40x

Percentage difference with respect of C = (40x/80x) × 100% = 50%

∴ The difference between A and B is 50% of C

Given:

A number increased by 32%

Calculation:

Let this number be P

P × (132/100) = 396

P = 100 × 3 = 300

Given:

A reduction of 20% in the price of sugar

Purchase to obtain 4 kg more for Rs.160

Calculation:

Let the original price per kg of sugar is Rs. x

Then the reduced price per kg = x × (80/100) = 4x/5

Quantity of sugar that can be bought for Rs.160 originally = Rs. 160/x

Quantity of sugar that can be bought for Rs.160 with reduced price = 160/(4x/5) = 800/4x

According to the question,

⇒ 800/4x = (160/x) + 4

⇒ (800/4x) – (160/x) = 4

⇒ (800 – 640)/4x = 4

⇒ 160 = 16x

⇒ x = 10

∴ The original price of sugar is 10 Rs. per kg 

Given:

Due to an increase of 40% in the price of eggs, 24 eggs less are available for Rs.560

Calculation:

Let, Price of per dozen eggs = Rs.10x

Let, Total purchase capacity initially = 10y dozen eggs

24 eggs = 2 dozen eggs

As question says,

(10x) × (10y) = 560

⇒ 10xy = 56      ----(I)

New price after reduction = {(100 + 40)/100} × 10x = Rs.14x

Final purchase capacity after reduction = (10y – 2) kg

As question says,

(14x) × (10y – 2) = 560

⇒ 10xy – 2x = 40      ----(II)

From equation (I) and (II)

56 – 2x = 40

⇒ x = 8

Present price per dozen of eggs = 14 × 8 = 112 Rs./dozen

∴ 112 Rs./dozen is original price of eggs.

Given:

Due to rise of 20% in the price of apples a dealer get 20 kg less for Rs.18,000

Calculation:

Let, Price of per kg apple = Rs.100x

Let, Total purchase capacity initially = 100y kg

As question says,

(100x) × (100y) = 18000

⇒ 100xy = 180      ----(I)

New price after reduction = {(100 + 20)/100} × 100x = Rs.120x

Final purchase capacity after reduction = (100y – 20) kg

As question says,

(120x) × (100y – 20) = 18000

⇒ 100xy – 20x = 150      ----(II)

From equation (I) and (II)

180 – 20x = 150

⇒ x = 1.5

New price of per kg apple = 120 × 1.5 = 180 Rs./kg

∴ 180 Rs./kg is reduction price of apple.

Given:

A person can buy 500g more sugar for Rs. 36 if the price of sugar is reduced by 20%.

Calculations:

Let the original price of sugar be Rs. x/kg.

Reduced price of sugar = 80% of x = (80/100) × x = (4/5) x

so \(\frac{36}{\frac{4x}{5}}\ - \frac{36}{x}\ = \ \frac{1}{2}\) (consumption = expenditure/price)

⇒  \(\frac{45}{x}\ -\ \frac{36}{x}\ =\ \frac{1}{2}\)

⇒ 9/x = 1/2

⇒ x= 18

∴ the original price of sugar is Rs. 18/kg.

Given:

Deepak’s total marks = 256

Chintu’s marks = 25% more than Deepak

Bittu’s marks = 10% less than Chintu

Asha’s marks = 25% more than Bittu

Calculations:

Let Deepak’s marks be 100

Chintu got 25% marks more than Deepak.

So, Marks obtained by Chintu = 125

Bittu got 10% marks less than Chintu.

So, Marks obtained by Bittu = 125 × (90/100)

Asha got 25% more marks than Bittu.

So, Marks obtained by Asha = 125 × (90/100) × (125/100) = 1125/8

Now, Deepak’s marks = 256

Marks obtained by Asha = (256/100) × (1125/8) = 360

∴ Asha got 360 marks out of 500.

Calculation:

Let this number be 100

Number increased by 20%

New number = 100 × (120/100) = 120

To get back the original number, new number should be reduced by = 120 – 100 = 20

Reduced % = (20/120) × 100 = 16.67%

∴ The new number should be reduced by 16.67% to get the original number

Given:

Due to rise of 20% in price of orange a dealer get 4 kg less for Rs.480

Calculation:

Let, Price of per kg orange = Rs.10x

Let, Total purchase capacity initially = 10y kg

As question says,

(10x) × (10y) = 480

⇒ 10xy = 48      ----(I)

New price after reduction = {(100 + 20)/100} × 10x = Rs.12x

Final purchase capacity after reduction = (10y – 4) kg

As question says,

(12x) × (10y – 4) = 480

⇒ 10xy – 4x = 40      ----(II)

From equation (I) and (II)

48 – 4x = 40

⇒ x = 2

Original price per kg of orange = 10 × 2 = 20 Rs./kg

∴ 20 Rs./kg is original price of orange.

Given:

In an election X got 30% of the total votes. Y got 25% of the total votes. Z got the remaining votes and he got 9600 more votes than X.

Formula:

Percentage increase/ decrease = [(new - actual)/actual] × 100%

Calculation:

Total no. of votes = 100%

⇒ X + Y + Z = 100%

⇒ 30% + 25% + Z = 100%

⇒ Z = 45%

And Z got 9600 more votes than X.

Z – X = 45% - 30% = 15%

15% = 9600

⇒ 1% = 640

And 100% = 64000 = total votes

Number of votes Y got = (25/100) × 64000 = 16000

∴ Number of votes Y got is 16000.

Given:

Amount of pulses to be bought = 50 kg

Reduced price of the pulses = 10%

Calculations:

Let original price = Rs. 100 per kg

Money required to buy 50 kg of pulses = Rs. (100 × 50) = Rs. 5000

New price = (100 – 10) = Rs. 90 per kg

The quantity of pulses bought = (5000/90) kg

⇒ 55.55 kg

∴ The quantity of pulses that can be bought is 55.55 kg.

Given:

Adding = 5%

Calculations:

Let the number be x.

After adding 5% of it, it becomes = x + x × (5/100) = 1.05x

Required percentage = (1.05x/x) × 100 = 105%

∴ The number is 105% of the original number.

Given:

Weight of statue = 160 kg

Copper = 50%

Zinc = 25%

Removed aluminium = 5%

Calculations:

Percentage of aluminium in statue = [100 – (50 + 25)]% = 25%

Weight of statue = 160 kg

Quantity of aluminium = 25% of 160 kg

⇒ (25/100) × 160

⇒ 40 kg

According to the question,​

⇒ 40 - (40)× 5%

⇒ 38 kg

∴ The quantity of aluminium requires to make the statue is 38 kg.

Given:

Maths marks = 40

Hindi marks = 45

English marks = 48

Science marks = 35

Civics marks = 47

Maximum mark for each subject = 50

Calculations:

Total marks obtained = 40 + 45 + 48 + 35 + 47 = 215

Maximum marks = 5 × 50 = 250

Overall Percentage = (215/250) × 100 = 86%

∴ The overall percentage of marks she got is 86%.

(b) Total marks = 500
Marks scored by Vikram = 500 × 72% = 360
Marks scored in Science
= 360 – [80 + 70 + 76 + 65] = 69

Given:

Fresh fruit contains 78% water and dry fruit contains 20% water.

Total quantity of fresh fruit = 100 kg

Total quantity of dry fruit = 100 kg

Concept used:

Dry fruit = (Pulp in fresh fruit/Pulp in dry fruit) × Total quantity of fresh fruit

Calculation:

Fresh fruit contains 78% water and dry fruit contains 20% water.

Fresh fruit has pulp = (100 - 78)% of fresh fruit

⇒ 22% of fresh fruit

⇒ 22% of 100 kg

⇒ 22 kg

Dry fruit has pulp = (100 - 20)% of dry fruit

⇒ 80% of 100 kg

Dry fruit obtained from fresh fruit = (Pulp in fresh fruit/Pulp in dry fruit) × Total quantity

⇒ (22 kg/80 kg) × 100 kg

⇒ 27.5 kg.

∴ Dry fruit that can be obtained from fresh fruit is 27.5 kg.

Given:

Salary increased by 18 % and decreased by 12 %.

Formula used:

Increase or decrease in salary = a – b – (ab/100)%

Where, positive sign means increment and negative sign means decrement

Calculation:

 ⇒ 18 – 12 – [(18 × 12)/100] %

 ⇒ (6 – 2.16)%

⇒ 3.84%

∴ There will be 3.84% increase in salary.

Given:

Votes received by two candidates in terms of ratio = 3 : 10

Total votes received = 156200

Calculation:

Let the votes got by two candidates be 3x & 10x

10x = 156200

⇒ x = 15620

Total votes polled = 3x + 10x

⇒ 13 × 15620 = 203060

∴ The total votes polled are 203060.

Given

Income of Karan = Rs.x

Income of Arjun = Rs.y

Calculation:

Expenditure on food by Karan = 10 % of x

Expenditure on entertain by Karan = 2(10 % of x)

20x/100

Saving of Karan = Rs.35,000

Income of Karan = expenditure + saving

⇒ x = (10x/100) + (20x/100) + 35,000

⇒70x/100 = 35,000

⇒ x = (35,000 × 100)/70

⇒ x = 50,000

Expenditure on food by Arjun = Rs.10 % of y

Expenditure on entertainment by Arjun = Rs.12,000

Saving of Arjun = Rs.75 % of y

Income of Arjun = 10 % of y + 12,000 + 75 % of y

⇒ y= 85 % of y + 12,000

⇒ 15y/100 = 12000

⇒ y = (12,000 × 100)/15

⇒ y = Rs.80,000

Given :

Anuja owns \( 66{ 2\ \over 3}\)% or (2/3) of a property   (\( 66{2 \ \over 3}\)% = 2/3)

30% of Anuja's owns property worth Rs. 125000

Calculations :

Let the worth of the property be 'x' 

According to the question 

30% of (2/3) of x = 125000 

⇒ x = Rs. 625000 

45% of 625000 = (45/100) of 625000 

⇒ Rs. 281250 

∴ The value of 45% of the total property will be Rs. 281250