Question

a student is asked to multiply a number by
$\frac{8}{17}$
instead of it , he divides the number by
$\frac{8}{17}$
and gets 225 more than the original result. the given number is ?​

Answer 1

Solution:-

Let us assume that the given number = x

Result when calculated rightly $= x\times \frac{8}{17}$

$= {\frac{8x}{17}}$

Result when calculated wrongly $= x\div \frac{8}{17}$

$= x\times \frac{17}{8}$

$= \frac{17x}{8}$

According to Question:-

$\frac{17x}{8}$ $= 225$$+ {\frac{8x}{17}}$

$\implies \frac{17x}{8}$$-{\frac{8x}{17}}$ $= 225$

L.C.M = 136

$\implies \frac{17x\times 17 - 8x\times 8}{136}$ $= 225$

$\implies \frac{289x - 64x}{136}$ $= 225$

$\implies \frac{225x}{136}$ $= 225$

$\implies {x=136}$

Verification:-

$x\div \frac{8}{17}$ $- x\times \frac{8}{17}$ $= 225$

$\implies 136\div \frac{8}{17}$ $- 136\times \frac{8}{17}$ $= 225$

$\implies 136\times \frac{17}{8}$ $- 8\times 8$ $= 225$

$\implies 17\times 17$ $- 64$ $= 225$

$\implies 289 - 64$ $= 225$

$\implies 225$ $= 225$

∴ L.H.S = R.H.S

∴ Given Number = 136

Answer 2

Answer:

Let us assume that the given number = x

Let us assume that the given number = xResult when calculated rightly = x\times \frac{8}{17}=x×178

= {\frac{8x}{17}}=178x

Result when calculated wrongly = x\div \frac{8}{17}=x÷178

= x\times \frac{17}{8}=x×817

= x\times \frac{17}{8}=x×817= \frac{17x}{8}=817x

According to Question:-

According to Question:-\frac{17x}{8}817x = 225=225 + {\frac{8x}{17}}+178x

\implies \frac{17x}{8}⟹817x -{\frac{8x}{17}}−178x = 225=225

L.C.M = 136

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136Verification:-

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136Verification:-x\div \frac{8}{17}x÷178 - x\times \frac{8}{17}−x×178 = 225=225

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136Verification:-x\div \frac{8}{17}x÷178 - x\times \frac{8}{17}−x×178 = 225=225\implies 136\div \frac{8}{17}⟹136÷178 - 136\times \frac{8}{17}−136×178 = 225=225

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136Verification:-x\div \frac{8}{17}x÷178 - x\times \frac{8}{17}−x×178 = 225=225\implies 136\div \frac{8}{17}⟹136÷178 - 136\times \frac{8}{17}−136×178 = 225=225\implies 136\times \frac{17}{8}⟹136×817 - 8\times 8−8×8 = 225=225

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136Verification:-x\div \frac{8}{17}x÷178 - x\times \frac{8}{17}−x×178 = 225=225\implies 136\div \frac{8}{17}⟹136÷178 - 136\times \frac{8}{17}−136×178 = 225=225\implies 136\times \frac{17}{8}⟹136×817 - 8\times 8−8×8 = 225=225\implies 17\times 17⟹17×17 - 64−64 = 225=225

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136Verification:-x\div \frac{8}{17}x÷178 - x\times \frac{8}{17}−x×178 = 225=225\implies 136\div \frac{8}{17}⟹136÷178 - 136\times \frac{8}{17}−136×178 = 225=225\implies 136\times \frac{17}{8}⟹136×817 - 8\times 8−8×8 = 225=225\implies 17\times 17⟹17×17 - 64−64 = 225=225\implies 289 - 64⟹289−64 = 225=225

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136Verification:-x\div \frac{8}{17}x÷178 - x\times \frac{8}{17}−x×178 = 225=225\implies 136\div \frac{8}{17}⟹136÷178 - 136\times \frac{8}{17}−136×178 = 225=225\implies 136\times \frac{17}{8}⟹136×817 - 8\times 8−8×8 = 225=225\implies 17\times 17⟹17×17 - 64−64 = 225=225\implies 289 - 64⟹289−64 = 225=225\implies 225⟹225 = 225=225

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136Verification:-x\div \frac{8}{17}x÷178 - x\times \frac{8}{17}−x×178 = 225=225\implies 136\div \frac{8}{17}⟹136÷178 - 136\times \frac{8}{17}−136×178 = 225=225\implies 136\times \frac{17}{8}⟹136×817 - 8\times 8−8×8 = 225=225\implies 17\times 17⟹17×17 - 64−64 = 225=225\implies 289 - 64⟹289−64 = 225=225\implies 225⟹225 = 225=225∴ L.H.S = R.H.S

\implies \frac{17x\times 17 - 8x\times 8}{136}⟹13617x×17−8x×8 = 225=225\implies \frac{289x - 64x}{136}⟹136289x−64x = 225=225\implies \frac{225x}{136}⟹136225x = 225=225\implies {x=136}⟹x=136Verification:-x\div \frac{8}{17}x÷178 - x\times \frac{8}{17}−x×178 = 225=225\implies 136\div \frac{8}{17}⟹136÷178 - 136\times \frac{8}{17}−136×178 = 225=225\implies 136\times \frac{17}{8}⟹136×817 - 8\times 8−8×8 = 225=225\implies 17\times 17⟹17×17 - 64−64 = 225=225\implies 289 - 64⟹289−64 = 225=225\implies 225⟹225 = 225=225∴ L.H.S = R.H.S∴ Given Number = 136