Question

Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?​

Answer 1

QUESTION 1:

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

SOLUTION:

• Let the greater number be x.

• Let the smaller number be y.

By data,

Sum of the two numbers is 95.

x + y = 95.

Let the above equation be equation 1.

Again by data,

The greater exceeds the smaller number by 15.

x = y + 15

Let the above equation be equation 2.

Substitute equation 2 in equation 1.

$x + y = 95 \\ \\ (y + 15) + y = 95 \\ \\ y + 15 + y = 95 \\ \\ 2y = 95 - 15 \\ \\ 2y = 80 \\ \\ y = \frac{80}{2} \\ \\ y = 40$

The smaller number is 40.

Substitute y = 40 in equation 2.

$x = y + 15 \\ \\ x = 40 + 15 \\ \\ x = 55$

The greater number is 55.

ANSWERS:

• The smaller number is 40.
• The greater number is 55.

QUESTION 2:

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

SOLUTION:

• Let the greater number be x.

• Let the smaller number be y.

By data,

Two numbers are in the ratio 5:3.

x : y = 5 : 3

$\frac{x}{y} = \frac{5}{3} \\ \\ x = \frac{5}{3} \times y \\ \\ x = \frac{5y}{3}$

Let the above equation be equation 1.

Again by data,

The numbers differ by 18.

x - y = 18

Let the above equation be equation 2.

Substitute equation 1 in equation 2.

$x - y = 18 \\ \\ \dfrac{5y}{3} - y = 18 \\ \\ \dfrac{5y - (3 \times y)}{3} = 18 \\ \\ \dfrac{5y - 3y}{3} = 18 \\ \\ \dfrac{2y}{3} = 18 \\ \\ 2y = 18 \times 3 \\ \\ 2y = 54 \\ \\ y = \dfrac{54}{2} \\ \\ y = 27$

The smaller number is 27.

Substitute y = 27 in equation 2.

$x - y = 18 \\ \\ x - 27 = 18 \\ \\ x = 18 + 27 \\ \\ x = 45$

The greater number is 45.

ANSWERS:

• The smaller number is 27.
• .The greater number is 45.

Answer 2

Answer:

Question No ❶ :-

• Sum of two numbers is 95. If one exceeds the other by 15. Find the numbers.

Given :

• Sum of two numbers is 95.
• One exceeds the other by 15.

To Find :-

• What is the numbers.

Solution :-

Let, the first number be x

And, the other number be x + 15

According to the question,

⇒ x + x + 15 = 95

⇒ 2x + 15 = 95

⇒ 2x = 95 - 15

⇒ 2x = 80

⇒ x = $\dfrac{\cancel{80}}{\cancel{2}}$

➠ x = 40

Hence, the required numbers are,

✧ First number = x = 40

✧ Other number = x + 15 = 40 + 15 = 55

$\therefore$ The numbers are 40 and 55 .

$\rule{300}{1.5}$

Question No ❷ :-

• Two numbers are in the ratio of 5:3. If they differ by 18. What are the numbers.

Given :-

• Two numbers are in the ratio of 5:3.
• They are differ by 18.

To Find :-

• What are the numbers.

Solution :-

Let, the first number be 5x

And, the second number be 3x

According to the question,

↦ 5x - 3x = 18

↦ 2x = 18

↦ x = $\dfrac{\cancel{18}}{\cancel{2}}$

➦ x = 9

Hence, the required numbers are,

✧ First number = 5x = 5(9) = 45

✧ Second number = 3x = 3(9) = 27

$\therefore$ The numbers are 45 and 27 .

$\rule{300}{1.5}$