Question

Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Then the numbers are:

(A) 40, 42                                           

(B) 42, 48

(C) 40, 48                                           

(D) 44, 50


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Answer 1

Answer: (C) 40,48

Explanation:

According to given information

x/y=5/6

=> 6x-5y=0 ........(I)

x-8/y-8=4/5

=> 5x-40=4y-32

=> 5x-4y=8 ...........(II)

from eq. (I)

6x-5y=0

=> x=5y/6

substituting in......(II)

5x-4y=8

=>5[5y/6]-4y=8

=>y/6=8

=>y=48

THEREFORE

x=5y/6

=>x=5×48/6

=> x=40

Answer 2

Let us consider the two numbers are x and y

______________

Given:

x/y = 5/6

x × 6 = y × 5

6x – 5y = 0………………..(1)

If 8 is subtracted from each of the numbers then the ratio is 4:5.

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

Then the equation is

5x – 4y = 8……………….(2)

From equation (1)

x = 5y/6

Substituting value of x in equation (2)

5(5y/6) – 4y = 8

y = 48

Substitute the value of y in equation (1) we get

6x – 5(48) = 0

6x = 240

x = 40

Therefore the numbers are 40 and 48.