Question

the cost of pen is rupees 16 whole 3 upon 5 and that of pencil is rupees 4 hole 3 upon 4 which cost more by how much?​

Answer 1

GIVEN :-

$\rm{ \: given \: that \: cost \: of \: :}$

$\rm{ \: cost \: of \: pen = 16 \frac{3}{5} \: \: rupees}$

$\rm{ \: cost \: of \: pencil = 4 \frac{3}{4} \: \: rupees}$

TO FIND :-

$\rm{ which \: cost \: more \: among \: pen \: and \: pencil}$

SOLUTION :-

FOR ANSWER WE NEED TO CONVERT MIXED FRACTION INTO IMPROPER FRACTION

FOR PEN :-

$\rm{ \: cost \: of \: pen = 16 \frac{3}{5} \: \: rupees}$

$\implies$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed { \rm{ a \frac{m}{n} \: = \frac{an \: + \: m}{n} }}}$

$\implies \rm{ 16 \frac{3}{5} = \frac{(16)(5) + 3}{5} }$

$\implies \rm{ 16 \frac{3}{5} = \frac{8 3}{5} }$

$\rm{ \: cost \: of \: pen = \frac{83}{5} \: \: rupees} - - - \: eq1$

NOW, FOR PENCIL :-

$\rm{ \: cost \: of \: pencil = 4 \frac{3}{4} \: \: rupees}$

$\implies$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed { \rm{ a \frac{m}{n} \: = \frac{an \: + \: m}{n} }}}$

$\implies \rm{ 4 \frac{3}{4} = \frac{(4) (4) + 3}{4} }$

$\implies \rm{ 4 \frac{3}{4} = \frac{19}{4} }$

$\rm{ \: cost \: of \: pencil = \frac{19}{4} \: \: rupees} - - - \: eq2$

NOW EQUALIZE THE DENOMINATORS OF EQUATION 1 AND EQUATION 2

FOR PEN :-

$\mathrm{ \: multiplying \: both \: numerator \: and \: denominator \: by \: 4}$

$\implies \mathrm{ \frac{83 \times 4}{5 \times 4}}$

$\implies \: \rm{ \frac{332}{20} }$

$\rm{ \: cost \: of \: pen = \frac{332}{20} \: \: rupees} - - - \: eq3$

FOR PENCIL :-

$\mathrm{ \: multiplying \: both \: numerator \: and \: denominator \: by \: 5}$

$\implies \mathrm{ \frac{19 \times 5}{4 \times5 }}$

$\implies \: \rm{ \frac{95}{20} }$

$\rm{ \: cost \: of \: pencil = \frac{95}{20} \: \: rupees} - - - \: eq4$

SO WE CAN SEE THAT PEN COSTS MORE THAN THE PENCIL,

NOW DIFFERENCE OF COSTS BETWEEN PEN AND PENCIL

SO SUBTRACTING EQ 4 FROM 3

$\implies \rm{ \frac{332}{20} - \frac{95}{20} }$

$\implies \rm{ \frac{332 - 95}{20} }$

$\implies \rm{ \frac{237}{20} } \: or \: 11.85$

HENCE ,

$\implies \boxed{ \boxed { \rm{pen \: costs \: \: \frac{237}{20} \: or \: 11.85 \: rupees \: more\: }}}$