WORD PROBLEMS ON FOUR BASIC OPERATIONS

Problem 1 :

There are 5 senior doctors 4 junior doctors in a hospital and each senior doctor has 3 nurses and each junior doctor has 2 nurses. How many nurses are working in the hospital?

Solution :

Number of nurses working in the hospital :

= 5x3 + 4x2

= 15 + 8

= 23

Problem 2 :

A box of pencils contains 50 pencils, a box of pens contains 40 pens and a box of erasers contains 30 erasers. Adam bought half of a box of pencils, one-fourth of a box of pens and one-third of a box of erasers. Find the total number of items he bought. 

Solution :

Total number of items :

= (1/2)(50) + (1/4)(40) + (1/3)(30)

= 25 + 10 + 10

= 45

Problem 3 :

In an company, there is one general manager and four managers. Each manager has six assistant managers and each assistant manager has seven personal assistants and each personal assistant controls ten employees. Find the total number of people working in the office.

Solution :

Number of people working in each category :

General manager : 1

Number of managers : 4

Number of assistant managers : = 4 x 6 = 24

Number of personal assistants : 24 x 7 = 168

Number of employees : 168 x 10 = 1680

Total number of people working in the company :

= 1 + 4 + 24 + 168 + 1680

= 1877

Problem 4 :

James had $6000. He kept three-fourth of the money for himself. He used three-fourth of the remaining for his monthly expanses and donated the rest to a charity. How much money did he donate to the charity?

Solution :

Given : James had $6000 and he kept three-fourth of the money for himself.

Remaining = 6000 - (3/4)6000

= 6000 - (0.75)6000

= 6000 - 4500

= 1500

Given : James used three-fourth of the remaining for his monthly expanses and donated the rest to a charity.

Amount of money James donated to the charity :

= (1/4)1500

= (0.25)1500

= $125

Problem 5 :

Jessica had some money. She gave one-fourth of the money to her brother and the rest to her sister. The money given to Jessica's sister is equal to $55 more than two times of the money given to her brother. Find the original amount of money that Jessica had. 

Solution :

Let x be the original amount of money that Jessica had.

Amount of money given to her brother = (1/4)x

Amount of money given to her sister = (3/4)x

Given : The money given to Jessica's sister is equal to $55 more than two times of the money given to her brother.

(3/4)x = 2[(1/4)x] + 55

3x/4 = x/2 + 55 

Multiply both sides by 4.

4(3x/4) = 4(x/2 + 55)

3x = 4(x/2) + 4(55)

3x = 2x + 220

Subtract 2x from both sides.

x = 220

The original amount of money that Jessica had is $220. 

Problem 6 :

The denominator of a fraction exceeds the numerator by 3. If 2 be added to both numerator and denominator, the fraction becomes 2/3. Find the fraction.

Solution :

Let x be the numerator of the fraction.

Then, the denominator is (x + 3).

Then, the fraction is

x/(x + 3)

Given : If 2 be added to both numerator and denominator, the fraction becomes 2/3.

(x + 2)/(x + 3 + 2) = 2/3

(x + 2)/(x + 5) = 2/3

3(x + 2) = 2(x + 5)

3x + 6 = 2x + 10

Subtract 2x from both sides.

x + 6 = 10

Subtract 6 from both sides.

x = 4

Therefore, the fraction is

= 4/(4 + 3)

= 4/7

Problem 7 :

If a person wants to become a journalist, he has to write notes at a rate of 100 words per minute. James was able to write only 50 words per minute when he started reporting. But through practice, he was able to increase his speed by 8 words per minute each month. Find the number of words per minute that James could write in 3 months.

Solution :

Number of words per minute that James could write in 3 months :

= 50 + 3x8

= 50 + 24

= 74

Problem 8 :

A taxi service charges a flat rate of $10 and $2.50 per mile. If Daniel uses the taxi service for 8 miles, find the amount he has to pay.

Solution :

Amount has to be paid by Daniel for 8 miles :

= 10 + 5x2.50

= 10 + 12.50

= $22.50

Problem 9 :

Lily divided 600 by 4, multiply the result by 3 and added 3 to the final answer. Kemka multiplied 600 by 2, divided the result by 4 and subtracted 7 from the final answer. Find the difference between the answers of Lily and Kemka.

Solution :

Lily :

= [(600/4)] x 3 + 3

= [150] x 3 + 3

= 450 + 3

= 453

Kemka :

= (600 x 2)/4 - 7

= 1200/4 - 7

= 300 - 7

= 293

Difference between the answers of Lily and Kemka :

= 453 - 293

= 160

Problem 10 :

Mr. David spent a total of $600 for staying in a hotel room. Each day of his staying, he bought a dinner at a restaurant for $25. If Mr. David spent a total of $775 for both staying and dinners, find the number of dinners he bought.

Solution :

Mr. David spent a total of $600 for staying in a hotel room and he spent a total of $775 for both staying and dinners.

Amount of money spent only for dinners :

= 775 - 600

= $175

The cost of 1 dinner was $25.

Number of dinners bought :

= 175/25

= 7

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