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# If 45 is subtracted from twice the greater of two numbers, it results in the other number. if 21 is subtracted from twice the smaller number, it results in the greater number. find the numbers

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One of the most important and conceptual question from linear equations in two variables in which we have to find the numbers if 45 is subtracted from twice the greater of two numbers, it results in the other number. if 21 is subtracted from twice the smaller number, it results in the greater number.

RS Aggarwal, Class 10, chapter 3E, question no 7

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1. Let the greater number be x and the smaller number be y.

Then, we have:

25x – 45 = y

or 2x – y = 45 ……….(i)

2y – 21 = x

or –x +2y = 21 ………(ii)

On multiplying (i) by 2, we get:

4x – 2y = 90 ………..(iii)

On adding (ii) and (iii), we get

3x = (90 + 21) = 111

⇒ x = 37

On substituting x = 37 in (i), we get  2 × 37 – y = 45

⇒ 74 – y = 45

⇒ y = (74 – 45) = 29

Hence, the greater number is 37 and the smaller number is 29.

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