Question

Two numbers are in the ratio 5 : 6. If 8 is
subtracted from each of the numbers, the
ratio becomes 4:5. The two numbers are
(a) 10, 12
(b) 20, 24
(C) 30, 36
(d) 40, 48
​

Answer 1

Step-by-step explanation:

initial ratio=5:6

so let the no. be 5x and 6x

new ratio=4:5

now,

$\frac{5x - 8}{6x - 8} = \frac{4}{5}$

cross multiply

$5(5x - 8) = 4(6x - 8)$

$25x - 40 = 24x - 32$

$25x - 24x = - 32 + 40$

$x = 8$

now the no. are 5x=5(8)=40 6x=6(8)=48

so the answer is 40,48

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Answer 2

Given :-

Ratio of the two numbers = 5 : 6

Ratio of the numbers if 8 is subtracted = 4 : 5

To Find :-

The value of the two numbers.

Solution :-

Let the two numbers be x and y

According to the question,

$\sf \dfrac{x}{y} =\dfrac{5}{6}$

$\sf x \times 6 = y \times 5$

Equation (1),

$\longrightarrow \sf 6x - 5y = 0 \qquad ...(1)$

Given that, if 8 if subtracted the ratio would be 4 : 5

$\sf \dfrac{x-8}{y-8} =\dfrac{4}{5}$

$\implies \sf 5x - 40 = 4y - 32$

Next, the equation (2),

$\sf 5x - 4y = 8 \qquad ...(2)$

Multiplying equation (1) and (2),

$\sf 24x-25y=0 \qquad ...(3)$

$\sf 24x-25y=40 \qquad ...(4)$

Subtracting equation (3) and (4),

$\sf x=40$

Hence, the value of x is 40

Substituting the value of x is the equation (1),

$\longrightarrow \sf 6 \times 40-5y=0$

$\sf =250=5y$

$=\sf y=\dfrac{240}{5}$

$\sf =y=48$

Hence, the value of y is 48

Therefore, the two numbers are 40 and 48