# Question-134145

Question Number 134145 by EDWIN88 last updated on 28/Feb/21
Commented by Ñï= last updated on 28/Feb/21
$${Any}\:{time}\:{any}\:\mathrm{2}\:{hands}\:{no}\:{coincide}.{I}\:{remember}. \\$$
Commented by mr W last updated on 28/Feb/21
$${please}\:{explain}\:{what}\:{you}\:{mean}\:{sir}! \\$$
Answered by mr W last updated on 28/Feb/21
$${assumed}\:{the}\:{hands}\:{move}\:{uniformly}. \\$$$${say}\:{x}\:{minutes}\:{past}\:\mathrm{2}. \\$$$${position}\:{of}\:{hour}\:{hand}:\:\mathrm{10}+\frac{{x}}{\mathrm{60}}×\mathrm{5} \\$$$${position}\:{of}\:{minute}\:{hand}:\:{x} \\$$$$\mathrm{10}+\frac{{x}}{\mathrm{60}}×\mathrm{5}={x} \\$$$${x}=\frac{\mathrm{120}}{\mathrm{11}}=\mathrm{10}\frac{\mathrm{10}}{\mathrm{11}} \\$$$$\Rightarrow\left({a}\right) \\$$
Commented by mr W last updated on 28/Feb/21
$${old}\:{style}\:{clocks}\:{have}\:{hands}\:{which} \\$$$${don}'{t}\:{move}\:{uniformly},\:{but}\:{stepwise}, \\$$$${see}\:{Q}\mathrm{17449} \\$$
Commented by EDWIN88 last updated on 28/Feb/21
$$\mathrm{yes}..\mathrm{thanks} \\$$
Answered by bobhans last updated on 28/Feb/21
$$\therefore\mathrm{The}\:\mathrm{time}\:\mathrm{when}\:\mathrm{hands}\:\mathrm{be}\:\mathrm{together} \\$$$$=\:\left(\mathrm{5}×\mathrm{n}×\frac{\mathrm{60}}{\mathrm{55}}\right)\:\mathrm{mins}\:\mathrm{past}\:\mathrm{n}\:\mathrm{o}'\mathrm{clock} \\$$$$\mathrm{Here}\:\mathrm{n}=\mathrm{2} \\$$$$=\:\mathrm{5}×\mathrm{2}×\frac{\mathrm{60}}{\mathrm{55}}\:=\:\frac{\mathrm{120}}{\mathrm{11}}\:=\:\mathrm{10}\:\frac{\mathrm{10}}{\mathrm{11}}\:\mathrm{mins}\:\mathrm{past}\:\mathrm{2} \\$$
Commented by EDWIN88 last updated on 28/Feb/21
$$\mathrm{thanks} \\$$