Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.

NCERT - Mathematics

Book: NCERT - Mathematics

Chapter: 2. Linear Equations in One Variable

Subject: Maths - Class 8^th

Q. No. 8 of Exercises 2.2

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Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.

Let the numbers are x, x + 1, x + 2

According to the question,

2x + 3x +3 + 4x + 8 = 74

9x = 74 - 8 - 3 = 63

Thus, the numbers are, 7, 8 and 9.

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Chapter Exercises

Exercises 2.1

Exercises 2.2

Exercises 2.3

Exercises 2.4

Exercises 2.5

Exercises 2.6

1

If you subtract from a number and multiply the result by you get What is the number?

2

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

3

The base of an isosceles triangle is cm. The perimeter of the triangle is What is the length of either of the remaining equal sides?

4

Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

5

Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?

6

Three consecutive integers add up to 51. What are these integers?

7

The sum of three consecutive multiples of 8 is 888. Find the multiples.

8

Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.

9

The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

10

The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

11

Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

12

Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

13

A rational number is such that when you multiply it by and add to the product, you get What is the number?

14

Lakshmi is a cashier in a bank. She has currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs 4,00,000. How many notes of each denomination does she have?

15

I have a total of Rs 300 in coins of denomination Re 1, Rs 2 and Rs 5. The number of Rs 2 coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?

16

The organisers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3,000. Find the number of winners, if the total number of participants is 63.