Question

4. The ratio of two numbers is 8: 5. If 8 is added to the greater number and 5 is
subtracted from the smaller number, the greater number becomes twice the
smaller number. Find the smaller number.
(2) 75
(3) 25
(4945
(1) 15​

Answer 1

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Answer 2

Answer:

Let the two required numbers be 8x and 5x.  

Obviously, 8x>5x.  

Add 8 to 8x and subtract 5 from 5x.  

The given problem states that the result of addition is two times (i.e., twice) the result of the subtraction.  

i.e.,  

8x+8=2(5x−5)  

Now, we have to find x. Distribute 2 over the term 5x-5.  

8x+8=2(5x)−2(5)  

⟹8x+8=10x−10  

Bring x terms to left hand side and constant terms to right hand side.

8x−10x=−10−8  

⟹−2x=−18  

⟹x=−18−2  

⟹x=9  

The required numbers are:  

8x=8×9=72 and  

5x=5×9=45.

(4) 45 is the correct option.

Step-by-step explanation:

Hope this answer will help you.