• # question_answer (a) Divide 34 into two parts in such a way that ${{\left( \frac{4}{7} \right)}^{th}}$of one part is equal to ${{\left( \frac{2}{5} \right)}^{th}}$of the other. (b) Which of the following equation are linear equation in one variable. (a) ${{x}^{2}}+x=1$                    (b) $2x-7=\frac{2}{3}$ (c) ${{x}^{2}}+\text{ }x=10~$                      (d) $x-15=3x$

 (a)  Let,             Ist part = x Then, IInd part $=\left( 34\text{ }-\text{ }x \right)~$ According to question, ${{\left( \frac{4}{7} \right)}^{th}}$ of Ist part ${{\left( \frac{2}{5} \right)}^{th}}$  of IInd part or             $\frac{4}{7}x=\frac{2}{5}(34-x)$ or             $20x\text{ }=\text{ }14\left( 34-x \right),$ [by cross multiplication] or         $~20x\text{ }=\text{ }14\text{ }x\text{ }34\text{ }-\text{ }14x$ or             $20x+14x=14\times 34$ or                        $34x=14\times 34$ or         $x=\frac{14\times 34}{34}$ or                     x=14 Hence, two parts are 14 and $34\text{ }-14\text{ }=\text{ }20$ i.e.,                    1st part = 14 and Und part = 20 (b) Linear equation in one variable are (c) $2x-7=\frac{2}{3}$and(d) $x-15=3x$