Given:

A person said 50% of his income.

After 1 year his income increases by 39% but still he saves the same amount as before.

Formula used:

Income = expenditure + savings

Calculations:

Let income be Rs. 100

He saves 50% of income = 50% × 100

= 39 × 2 = 78%

∴ The answer is 78%.

Given:

Ratio of Sum of Aman, Bharat, and Chandu = (2/9) ∶ (3/7) ∶ (4/11)

Share of Chandu = Rs. 4284

Concept Used:

We need to take the L.C.M. of denominator of given ratios and multiply that L.C.M. with ratios to get ratios in whole number.

We need to equate the Ratios to their actual values.

Calculation:

 L.C.M. of (9, 7, 11) i.e. 693

Ratio = [(2/9) ∶ (3/7) ∶ (4/11)] _{× 693} = 154 ∶ 297 ∶ 252

Share of Chandu = 252 Units

⇒ 252 Units = Rs. 4284

⇒ 1 Unit = 4284/252 = RS 17

Difference between share of Aman and Bharat = (297 - 154) = 143 Units

⇒ Difference between share of Aman and Bharat = 143 × 17

⇒ Difference between share of Aman and Bharat = Rs. 2431

∴ The Difference between share of Aman and Bharat is Rs. 2431

Given:

Inlet pipe x and y can fill an empty tank in 20 hours and 30 hours.

Outlet pipe z can empty a full tank in 60 hours.

Concept used:

Time ∝ 1/Efficiency

Calculation:

The efficiency of pipe x is

⇒ x = 1/20

The efficiency of pipe y is

⇒ y = 1/30

The efficiency of pipe z will be negative because z is the outlet pipe

⇒ z = -1/60

Together they will fill the tank in

⇒ 1/20 + 1/30 - 1/60

⇒ (3 + 2 - 1)/60

⇒ 4/60

⇒ 1/15

∴ Together they will fill the tank in 15 hours.

Given:

The average weight of 6 men = 65.1667 kg

The average weight of 8 women = 78.125 kg

The average weight of 5 boys = 55.2 kg

Concept used:

• The decimal to fraction conversion:

• Average weight of n person = (Sum of weight of all n person)/(n number of persons)

Calculation:

According to the question,

The average weight of 6 men = 65.1667 kg = 65 + 0.1667

Given:

Four litres of liquid is drawn out of this vessel and is replaced with water. The ratio of the special liquid to the water becomes 1 : 2

Calculation:

Let x be the quantity of special liquid filled in vessel

⇒ 4 litres drawn so new quantity will be = x – 4

⇒ Quantity of water added = 4 litres

⇒ Ratio = (x – 4)/4

⇒ 1/2 = (x – 4)/4

⇒ 2x – 8 = 4

⇒ x = 12/2 = 6

∴ capacity of the vessel is 6 lit.

Given:

40 workers can build a dam in 30 days

60 workers are to be assigned to complete the same work

Formula used:

Efficiency = work done/Time taken

Calculation:

Let the number of days be x

40 workers can build a dam in 30 days = 40 × 30

⇒ 1200

Now,

60 Workers are to be assigned to be complete the same work 

⇒ x = 1200/60

⇒ 20 days

∴ The number of days required will be 20

Given:

A alone can complete a piece of work in 12 days.

A and B together can complete it in 8 days

Formula:

(A + B)’s 1 day work = 1/A + 1/B

Calculations:

A's 1 day's work = 1/12

(A + B)'s 1 day's work = 1/8

(A + B)'s 1 day's work = 1/12 + 1/B

⇒ 1/8 = 1/12 + 1/B

⇒ 1/8 – 1/12 = 1/B

⇒ 4/96 = 1/B

⇒ 1/B = 1/24

⇒ B = 24 Days

∴ B will finish the work in 24 days.

Alternate Method

Total work = LCM of 12 and 8 = 24

⇒ Total work = 24 units

In 1 day A can do 24/12 = 2 unit work

In 1 day A & B together can do 24/8 = 3 unit work

⇒ In 1 day B can do (3 - 2) = 1 unit work

⇒ To complete 24 unit work B alone will take 24/1 = 24 days

∴ B will finish the work in 24 days.

Given:

When a 30% concentration of alcohol is mixed with an 80% concentration of alcohol we get a mixture of 50% concentration of alcohol. 

Formula:

Mixture and Allegation method:

Calculation:

According to the above formula

Required ratio = 30 ∶ 20 = 3 ∶ 2

∴ The required ratio is 3 ∶ 2.

If an amount P is compounded at interest rate of r for T years then the total amount which we will get

And the compound interest which we will obtain

When the interest is compounded semiannually means, interest is added to principal amount every 6 month. In this case time cycle = 2 × 2 = 4 and effective rate = 10/2 = 5%

Now interest obtained in this case = 10000(1 + 5/100)⁴ – 10000 = 12155 – 10000 = Rs 2155

Now when interest is compounded biannually then in this case time cycle = 2/2 = 1 and effective rate = 10 × 2 = 20%

Now interest obtained in this case = 10000(1 + 20/100) – 10000 = 12000 – 10000 = Rs 2000

So the difference is,   2155 – 2000 = Rs 155.