Q4 of 80 Page 48

A number is divided into two parts such that one part is 10 more than the other. If the two parts are in the ratio 5:3, find the number and the two parts.

A number is divided into two parts.

The two parts are in the ratio 5:3.


Let the common multiple be x.


The two parts will then be 5x and 3x.


One part is 10 more than the other part.


According to the given condition,


5x = 3x + 10


⇒ 5x – 3x = 10 (Transposing 3x to LHS)


2x = 10


⇒ x = (Transposing 2 to RHS)


x = 5


The two parts of the number are


3x = 3 × 5 = 15


5x = 5 × 5 = 25


The number = 15 + 25 = 40


∴ The number is 40 and its two parts are 15 and 25.


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