Statement Problems on Integers using all Fundamental Operations

Statement Problems on Integers using all Fundamental Operations.

We have learned how to add, subtract, multiply and divide integers. This section will review the rules learned for operations with integers.

All the mathematical problems are life oriented problems.

Situation 1

If a person’s initial balance is ₹ 530 in a particular month. In the same month if he deposits ₹ 230 withdraws ₹ 150, again a withdrawal of ₹ 200 and a deposit of ₹ 99.

How will you find the answer for this?

Situation 2

If a person buys 8 pens for 80 rupees and he sells 4pens with a profit of ₹ 3 per pen and 3 pens with a loss of ₹ 2 per pen and one pen at the buying cost, find the total loss or profit of him.

Do you have any idea to approach this problem?

To solve all the statement problem, the following steps may be followed.

(i) Read the problem thoroughly.

(ii) Write down what is given.

(iii) Find out what they are asking.

(iv) Use the required formulae or easy way to attain the answer.

(v) Apply it.

(vi) Solve it.

(vii) Arrive the answer.

(viii) If possible check your answer.

Let us approach the above two situations as given below:

Example 1.28

Ferozkhan collects ₹1150 at the rate of ₹ 25 per head from his classmates on account of the 'Flag Day' in his school and returns ₹ 8 to each one of them, as instructed by his teacher. Find the amount handed over by him to his teacher.

Solution

Ferozkhan collects ₹1150 at the rate of ₹ 25 per head from his classmates on account of the 'Flag Day'

Total amount collected = ₹1150

Amount per head = ₹ 25

Number of students = 1150 ÷ 25 = 46

Amount returned to each student is ₹ 8

Amount returned to 46 students = 46 × 8 = ₹ 368

Amount handed over to the class teacher

= ₹ 1150

 ₹ 368 (–)

 _____

 ₹ 782

 _____

Amount handed over to the class teacher = ₹ 782

Example 1.29

Each day, the workers drill down 22 feet further until they hit a pool of water. If the water is at 110 feet, on which day will they hit the pool of water?

Solution

Depth drilled in one day = –22 feet

Depth of water = –110 feet

Number of days required = –110 ÷ –22 = 5

Hence the workers wil reach resource in 5 days.

Example 1.30

How many years are between 323 BC(BCE) and 1687 AD(CE)?

Solution

Years in AD(CE) are taken as positive integers and BC(BCE) as negative integers.

Therefore, the difference is

= 1687 – (–323)

= 1687 + 323 = 2010 years