Question

. 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.​

Answer 1

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

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Then, we have :

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• 25x – 45 = y or 2x – y = 45 ﹏﹏(i)
• 2y - 21 = x or –x +2y = 21 ﹏﹏(ii)

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On multiplying (i) by (ii), we get:

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• 4x - 2y = 90 ﹏﹏(iii)

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

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$\:\:\:\:\:\dashrightarrow\:\sf{3x\: = \:(90\: +\: 21) \:= \:111}$

$\:\:\:\:\:\dashrightarrow\:\sf{x \:= \:37}$

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On substituting x = 37 in (i), we get

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$\:\:\:\:\:\dashrightarrow\:\sf{2 \:×\: 37\: - \:y\: = \:45}$

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$\:\:\:\:\:\dashrightarrow\:\sf{ 74\: -\: y \:=\: 45 }$

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$\:\:\:\:\:\dashrightarrow\:\sf{y \:= \:(74 \:-\: 45)\: = \:29 }$

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$\:\therefore\:{\underline{\sf{Hence, \:the \:greater \:number \:is\:{\textsf{\textbf{37 }}}\:and\:the\:smaller\:number\:is\:{\textsf{\textbf{29}}}}}}.$

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