Master Math: 4 Essential Solved Word Problems on Time, Age, and Profit/Loss

 1. Ram takes twice as much time as Shyam and thrice as much time as Krishna to finish a piece of work. If they can finish the work together in 16 days, how many days will each take to finish it alone?

Solution:

Let the time taken by Ram be x days.

• Time taken by Shyam = x/2 days
• Time taken by Krishna = x/3 days

Their 1-day work:

• Ram: 1/x
• Shyam: 2/x
• Krishna: 3/x

Combined 1-day work = 1/16

or, 1/x + 2/x + 3/x = 1/16

or, 6/x = 1/16

or, x = 96

Results:

• Ram: 96 days
• Shyam: 96/2 = 48 days
• Krishna: 96/3 = 32 days

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2. Sushila's monthly income is Rs. 18,000. She spends 1/5 on snacks, 3/10 on clothes, and 2/5 on transportation. What fraction does she save, and what is the savings amount?

Solution:

Total Expenditure Fraction = 1/5 + 3/10 + 2/5 = 9/10

• Savings Fraction: 1 - 9/10 = 1/10
• Savings Amount: 1/10 of 18,000 = Rs. 1,800

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3. Three years ago, the sum of the ages of a father and his son was 48 years. In three years from now, the ratio of their ages will be 3:1. What are their current ages?

Solution:

Let the current ages of the father and son be x and y.

Condition 1: 3 years ago

(x - 3) + (y - 3) = 48

or, x + y - 6 = 48

or, x + y = 48 + 6

or, x + y = 54

or, x = 54 - y .... (i)

Condition 2: 3 years from now

{x + 3} : {S + 3} = 3 : 1

or, {x + 3} / {y + 3} = 3/1

or, x + 3 = 3y + 9 .... (ii)

(Substitute x = 54 - y into the second equation)

or, (54 - y) - 3y = 9 - 3

or, 54 - y - 3y = 6

or, - 4y = - 48

or, y = 12

now, x = 54 - 12 = 42

(Substitute y = 12 into the first equation)

Results:

• Father's current age: 42 years
• Son's current age: 12 years

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4. By selling a watch for Rs. 4,500, a wholesaler suffers a 10% loss. At what price must he sell it to earn a 10% profit?

Solution:

Step 1: Find the Cost Price (CP)

Selling Price (SP) = Rs. 4,500

Loss = 10%

CP = {SP times 100} / {100 - Loss %}

       = {4500 times 100} / {90}

       = 50 times 100

       = Rs. 5,000

Step 2: Find the New Selling Price for 10% Profit

Target Profit = 10%

New SP = (100+10) % of CP

                 = (110/100) x Rs. 5,000

                 = 1.1 x Rs. 5,000

                 = Rs. 5,500 

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Practice Set

1. Aayush takes twice as long as Binod and four times as long as Chirag to complete a task. If all three working together can finish the task in 12 days, how many days would it take Binod to finish the work alone?

2. A person earns Rs. 40,000 per month. They spend 1/4 on rent, 2/5 on food, and 1/10 on entertainment.

• What fraction of the income is saved?
• What is the total amount spent on food and rent combined?

3. Five years ago, the sum of the ages of a mother and her daughter was 40 years. In five years from now, the mother will be exactly twice as old as the daughter. Find their current ages.

4. By selling a mobile phone for Rs. 18,000, a shopkeeper loses 20%.

• What was the cost price of the phone?
• At what price should they sell it to make a 15% profit?