Question Number 114863 by mathdave last updated on 21/Sep/20
$${find}\:{four}\:{consecutive}\:{multiples}\:{of}\:\mathrm{5} \\ $$$${such}\:{that}\:{twice}\:{the}\:{sum}\:{of}\:{the}\:{two} \\ $$$${greatest}\:{integer}\:{exceed}\:{five}\:{times}\:{the} \\ $$$${least}\:{by}\:\mathrm{5} \\ $$
Answered by PRITHWISH SEN 2 last updated on 21/Sep/20
$$\mathrm{let}\:\mathrm{the}\:\mathrm{integrs}\:\mathrm{are} \\ $$$$\:\:\:\:\:\:\:\:\:\left(\mathrm{5}\boldsymbol{\mathrm{m}}−\mathrm{10}\right),\left(\mathrm{5}\boldsymbol{\mathrm{m}}−\mathrm{5}\right),\mathrm{5}\boldsymbol{\mathrm{m}},\left(\mathrm{5}\boldsymbol{\mathrm{m}}+\mathrm{5}\right) \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{problem} \\ $$$$\:\:\:\mathrm{2}\left\{\mathrm{5m}+\left(\mathrm{5m}+\mathrm{5}\right)\right\}=\mathrm{5}\left(\mathrm{5m}−\mathrm{10}\right)+\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\Rightarrow\boldsymbol{\mathrm{m}}=\:\mathrm{11} \\ $$$$\:\:\:\:\:\therefore\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{are}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{45},\mathrm{50},\mathrm{55},\mathrm{60} \\ $$