Step by step solution for problem on Number system

Introduction

Problems on the number system are not that difficult it's like playing with the numbers, number systems includes square root formulas. Learn now and play with the numbers from today using Nithra Jobs. There are hundreds of companies and thousands of jobs hiring for job candidates in Tamil Nadu. Soon apply!!

Formulas:

(a + b) (a - b) = (a² - b²)

(a + b)² = (a² + b² + 2ab)

(a - b)² = (a² + b² - 2ab)

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a³ + b³) = (a + b) (a² - ab + b²)

(a³ - b³) = (a - b) (a² + ab + b²)

(a³ + b³ + c³ - 3abc) = (a + b + c) (a² + b² + c² - ab - bc - ac) When a + b + c = 0, then a³ + b³ + c³ = 3abc.

Solved Problems

1. The price of 70 Apples is equal to that of 140 Oranges. The price of 60 Apples and 75 Oranges together is Rs. 2535. The total price of 20 Apples and 40 Oranges is?

Answer: Rs.1040

Explanation:

70 Apples = 140 Oranges

1 Apple = ( 140 / 70 )

1 Apple = 2 Oranges

Oranges = 2 Oranges

Price of an 1 Apple = Price of 2 Oranges

Price of [ 60 Apples + 75 Oranges ] = Rs. 2535

60 Apples + 75 Oranges = 2535

60 ( 2 Oranges) + 75 Oranges = 2535

120 Oranges + 75 Oranges = 2535

195 Oranges = 2535

Orange = 2535 / 195

= 13

Price of an orange = Rs.13

Price of an Apple = 2 Oranges

= 2 × 13

= Rs.26

Price of an Apple = Rs.26

The total price of 20 Apples and 40 Oranges = ( 20 × 26 ) + (40 × 13)

= 520 + 520

= Rs.1040

The total price of 20 Apples and 40 Oranges = Rs.1040

2. The price of 4 tables and 5 chairs is Rs. 3360. With the same money one can buy 3 tables and 9 chairs. If one wants to buy 1 table and 1 chair, how much does he need to pay?

Answer: Rs.800

Explanation:

4 tables + 5 chairs = Rs.3360

With the same money one can buy, 3 tables + 9 chairs = Rs.3360

4 tables + 5 chairs = 3 tables + 9 chairs

( 4 - 3 ) tables = ( 9 - 5 ) chairs

1 table = 4 chairs

4 × ( 4 chairs ) + 5 chairs = Rs.3360

16 chairs + 5 chairs = 3360

21 chairs = 3360

Chair = 3360 / 21

= Rs.160

1 table + 1 chair = 4 chairs + 1 chair

= 5 chairs

= 5 × 160

= Rs.800

Price of 1 table and 1 chair = Rs.800

3. There are 5 working days in a regular week and for each day, the working hours are 10. A man earns Rs. 2.50 per hour for regular work and Rs. 12.5 per hour for overtime. If he earns Rs. 550 in 4 weeks, how many hours did he work?

Answer: 204 hours

Explanation:

[ weeks - 4, working days - 5 days in a week, hours - 10 ]

Regular working hours in 4 weeks = 4 × ( 5 × 10 )

= 4 × 50

= 200 hours

Amount earned by working in these regular working hours = 200 × 2.50

= Rs.500

Additional amount earned = 550 - 500

= Rs.50

Overtime hours worked = 50 / 12.5

= 4 hours

Total hours worked = 200 + 4

= 204 hours

Total hours worked = 204 hours

4. Find the value of 96² + 63² = (?)² - 111² - 8719

Answer: 185

Explanation:

Assume, the value be x.

96² + 63² = x² - 111² - 8719

x² = 12321 + 9216 + 12321 + 3969 + 8719

x² = 34225

The value of x is = 185

5. A man has Rs.720 in the denominations of one-rupee notes, two-rupee notes and five-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?

Answer: 270

Explanation:

Let the number of notes be x , 2x, and 5x.

Then, x + 2x + 5x = 720

8x = 720

x = 720/8

x = 90

Here, the number of notes of each denomination is equal, then multiply by 3 To find the total number of notes

So, the total number of notes = 3x

= 3 × 90

= 270

The total number of notes = 270

Conclusion:

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