Question

If the smaller one divides three times the larger of two numbers, we get 4 as quotient and 3 as the remainder. Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the numbers.
*pl.no substitute.

Answer 1

Dear Student,


$$\begin{gathered} letsmallerno.be\text{'}s\text{'}andlargerno.be\text{'}l\text{'} \\ Accordingtoquestion, \\ If\frac{3l}{s}isperformed4asaquotientand3asremainderisobtained \\ \Rightarrow 3l=4s+3 \\ \Rightarrow 3l-4s=3........................\overline{)1} \\ Also, \\ If\frac{7s}{l}isperformed5asaquotientand1asremainderisobtained \\ \Rightarrow 7s=5l+1 \\ \Rightarrow -5l+7s=1........................\overline{)2} \\ multiplying\overline{)1}by5and\overline{)2}by3andadding \\ \Rightarrow 5(3l-4s)+3(-5l+7s)=(3\times 5)+(1\times 3) \\ \Rightarrow \cancel{15l}-20s-\cancel{15l}+21s=15+3 \\ \Rightarrow s=18 \\ puttings=18in\overline{)1} \\ \Rightarrow 3l=3+(4\times 18) \\ \Rightarrow l=\frac{3+72}{3} \\ \Rightarrow l=\frac{75}{3} \\ \Rightarrow l=25 \\ So,largerno.is25andsmallerno.is18 \end{gathered}$$

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