Question

Marks obtained by two students are in the ratio of 7 5. The product of their marks is 2835. What are the total marks obtained by both the students together?​

Answer 1

Answer:

The sum of their marks is 108.

Step-by-step explanation:

Given :

Ratio of marks obtained by 2 students = 7 : 5

Product of their marks = 2835

To find :

The sum of their marks

Solution :

Let the marks be -

• 7x
• 5x

★ $\boxed{\sf{7x \times 5x = 2835}}$

$\sf{\longrightarrow} \:7x \times 5x = 2835 \\ \sf{\longrightarrow} \: {35x}^{2} = 2835 \\ \sf{\longrightarrow} \: {x}^{2} = \frac{2835}{35} \\ \sf{\longrightarrow} \: {x}^{2} = 81 \\ \sf{\longrightarrow} \:x = \sqrt{81} \\ \sf{\longrightarrow} \:x = 9$

$\rule{300}{1.5}$

★ Value of 7x

$\sf{\longrightarrow} \:7(9) \\ \sf{\longrightarrow} \:63$

Marks of one student = 63

$\rule{300}{1.5}$

★ Value of 5x

$\sf{\longrightarrow} \:5(9) \\ \sf{\longrightarrow} \:45$

Marks of another student = 45

$\rule{300}{1.5}$

★ The sum of their marks :

$\sf{\longrightarrow} \:45 + 63 \\\sf{\longrightarrow} \: 108$

$\therefore$ The sum of their marks is 108.

Answer 2

Explanation:-

Given :-

Marks obtained by two students are in the ratio 7 : 5.

Product of marks = 2835

To find :-

The total marks .

Solution:-

Let the marks obtained in ratio be 7x and 5x.

A/Q

• Their product is 2835.

→$7x \times 5x = 2835$

→$35x^2 = 2835$

→$x^2 = \dfrac{2835}{35}$

→$x^2 = 81$

→$x^{\cancel{2}}= (9)^{\cancel{2}}$

→$x = 9$

• Marks of each student.

7x = 7 × 9 = 63

5x = 5 × 9 = 45

Total marks obtained will be :-

→ 63 + 45

→ 108