Question

2. What should be added to the ratio 5 : 11, so that the ratio becomes 3 : 4?
3. Two numbers are in the ratio 7 : 5. If 2 is subtracted from each of them,
the ratio becomes 3 : 2. Find the numbers.
4. Two numbers are in the ratio 3: 7. If their sum is 710, find the numbers.
5. Find the ratio of A : B: C when
(a) A: B = 3:5 A: C = 6:7
(b) B: C = 1/2: 1/6 A:B = 1/3 : 1/5​

Answer 1

2.

Let the numbers be 5x and 11x.

By adding y to the ratio becomes 4 : 5

➣ ( 5x + y ) : ( 11x + y ) = 3 : 4  

➣ 4(5x + y) = 3(5x + y)  

➣ 20x + 4y = 15x + 3y

➣ 20x - 15x = -4y + 3y

➣ 5x = -y

3.

To Find:-

• Find the two numbers.

Solution:-

Given,

• Two numbers are in ratio of 7 : 5 and if 2 is subtracted the ratio of them will be 3 : 2.

Let the two numbers be 7x and 5x.

➣ (7x - 2)/(5x - 2) = 3/2

➣ 2(7x - 2) = 3(5x - 2)

➣ 14x - 4 = 15x - 9

➣ 9 - 4 = 15x - 14x

➣ x = 5

➣ $\boxed{\bf{\color{yelow}{ \: x \: = \: 5 \: }}}$

Therefore the value of x = 5

So,

The numbers are 7x = 7(5) ⟹ 35

The numbers are 5x = 5(5) ⟹ 25

Verification:-

Th ratio become 3 : 2  = 35 +

- 2 => 33

25 - 2 => 22

∴ The numbers are 33 and 22.

4.

Given:-

• Two numbers are in the ratio 3: 7 and their sum is 710.

Let the unknown number be x

3x + 7x = 710

10x = 710

x = 710/10

x = 71

Verification:-

3(71) + 7(71) = 710

213 + 497 = 710

710 = 710

Answer 2

$\huge\mathbb{\purple{Answer ♡ }}$

$\huge\sf\underline{\underline{\pink{Question 2}}}$

Let the numbers be 5x and 11x.

By adding y to the ratio becomes 4 : 5

➣ ( 5x + y ) : ( 11x + y ) = 3 : 4

➣ 4(5x + y) = 3(5x + y)

➣ 20x + 4y = 15x + 3y

➣ 20x - 15x = -4y + 3y

➣ 5x = -y

$\huge\mathbb{\orange{Answer 3 }}\star{}$

Two numbers are in ratio of 7 : 5 and if 2 is subtracted the ratio of them will be 3 :

Let the two numbers be 7x and 5x.

➣ (7x - 2)/(5x - 2) = 3/2

➣ 2(7x - 2) = 3(5x - 2)

➣ 14x - 4 = 15x - 9

➣ 9 - 4 = 15x - 14x

➣ x = 5

➣ x=5

Therefore the value of x = 5

So,

The numbers are 7x = 7(5) ⟹ 35

The numbers are 5x = 5(5) ⟹ 25

$\huge\mathbb{\red{Answer 4 }}$

Let the unknown number be x

3x + 7x = 710

10x = 710

x = 710/10

x = 71

${\huge{\fcolorbox{white}{WHITE}{♡HAN JU HUI♡}}}$