Question

a shopkeeper earns a profit of rs 5 by selling a notebook and incurs a loss of 50 paise per pencil and eraser while selling these from old stock on a particular day she earns a profit of 30 . If she sold 10 notebooks and the numbers of pencil and erasers she sold are in the ratio 6:4 find the number of pencil and eraser sold on that day​

Answer 1

In Angle PQR

In Angle PQR∠PSR = 90°

In Angle PQR∠PSR = 90°∠SPR = 30°

In Angle PQR∠PSR = 90°∠SPR = 30°∠SRP = 60° ... ( Remaining Angle )

In Angle PQR∠PSR = 90°∠SPR = 30°∠SRP = 60° ... ( Remaining Angle )∴ 30 - 60 - 90 ... Theorem

$\tt{\implies SP = \dfrac{1}{2} \times pr ...(side \: opposite \: to \: 30° \: angle)}$

$\tt{\implies 6 = \dfrac{1}{2} \times pr }$

$\tt{\implies pr = {6} \times {2} \ }$

$\tt{\implies pr = {12} \ }$

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$\tt{\implies sp = \dfrac{ \sqrt{3}}{2} \times pr ...(Side\: Opposite\: to\: 60°\: Angle)}$

$\tt{\implies sp = \dfrac{ \sqrt{3}}{2} \times pr }$

$\tt{\implies sp = \dfrac{ \sqrt{3}}{2} \times 12 }$

$\tt{\implies sp = {6 \sqrt{3\:unit}}\ }$

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