Question

b) Two numbers are in the ratio 7:5. When 10 is subtracted from each term, their ratio becomes 3:2. Find the numbers. ​

Answer 1

Answer:

x is 70, y is 50

Step-by-step explanation:

x:y = 7:5

x-10:y-10 = 3:2

solving both we get

x=70 y=50

Answer 2

The number are 70 and 50

Explanation -:

Given :

• The ratio of two numbers = 7 : 5
• 10 is subtracted from each
• New ratio of two numbers = 3 : 2

To Find :

• The two numbers

Solution :

Two numbers are in the ratio 7 : 5

Let the number be 7x and 5x

If 10 is subtracted from each other the ratio becomes 3 : 2

$\small\rm \bf{7x - 10 : 5x - 10 = 3 : 2}$

$⇢ \small\rm{ \dfrac{7x - 10}{5x - 10} = \dfrac{3}{2} }$

$⇢ \small\rm{ 3(5x - 10)= 2(7x - 10) }$

$⇢ \small\rm{ 15x - 30= 14x - 20 }$

$⇢ \small\rm{15x - 14 = 30 - 20}$

$⇢ \small\rm{x = 10}$

First number = 7x = 7 × 10 = 70

Second number = 5x = 5 × 10 = 50

The number are 70 and 50

Verifying -:

$\small\rm{7x - 10 \ratio \: 5x - 10 = 3 \ratio \: 2}$

$⇢ \small\rm{7 (10) - 10 \ratio \: 5 (10) - 10 = 3 \ratio \: 2}$

$⇢ \small\rm{70 - 10 \ratio \: 50 - 10 = 3 \ratio \: 2}$

$⇢ \small\rm{60 \ratio \: 40 = 3 \ratio \: 2}$

$⇢\small\rm{6 \ratio \: 4 =3 \ratio \: 2}$

$⇢ \small\rm{3 \ratio \: 2 =3 \ratio \: 2 }$

Hence, proved