Question

Two numbers are in the ratio 9:7. If 14 is subtracted from each. The ration becomes 7:5, Find
the numbers.​

Answer 1

Let number 1 = X
Let number 2 = Y

X/ Y = 9/7
X = 9Y/7

X -14 / Y -14 = 7/5
5X - 70 = 7 Y - 98
45Y/7 = 7 Y -28
45Y = 49Y - 196
Y = 49
So, X = 63

Answer 2

Two numbers are 63 and 49

Given :

• Two numbers are in the ratio 9 : 7

• When 14 is subtracted from each, the ratio becomes 7 : 5

To find :

The numbers

Solution :

Step 1 of 2 :

Form the equation

Two numbers are in the ratio 9 : 7

Let the numbers are 9x and 7x

Now it is given that when 14 is subtracted from each, the ratio becomes 7 : 5

By the given condition

$\displaystyle \sf{ (9x - 14):(7x - 14) = 7 : 5 }$

Step 2 of 2 :

Find the numbers

$\displaystyle \sf{ (9x - 14):(7x - 14) = 7 : 5 }$

$\displaystyle \sf{ \implies \frac{9x - 14}{7x - 14} = \frac{7}{5} }$

$\displaystyle \sf{ \implies 49x - 98 = 45x - 70 }$

$\displaystyle \sf{ \implies 49x - 45x = 98 - 70 }$

$\displaystyle \sf{ \implies 4x = 28 }$

$\displaystyle \sf{ \implies x = 7 }$

First number = 9x = 9 × 7 = 63

Second number = 7x = 7 × 7 = 49

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