Question

two equal sums of money were lent at s.i 11%p.a for 3½ years and 4½ years respectively. if the differences in interests for two perioeds was rs412.50 find each sum


rahul whose in ur dp​

Answer 1

${\huge{\bf{\orange{Required~Solution-:}}}}$

Let x be the principle that's taken on intrest.

${\sf{\pink{Simple~intrest~for}}}$ ${\sf{\pink3{\frac\pink{1}{\pink2}}}}$${\sf{\pink{years-:}}}$

$\blue\implies$${\sf{\blue{\frac{PRT}{100}}}}$ = ${\sf{\blue{\frac{x×11×7}{100×2}}}}$ = ${\sf{\blue{\frac{77x}{200}}}}$-----(1)

${\sf{\pink{Simple~intrest~for}}}$ ${\sf{\pink4{\frac\pink{1}{\pink2}}}}$${\sf{\pink{years-:}}}$

$\blue\implies$

$\blue\implies$${\sf{\blue{\frac{PRT}{100}}}}$ = ${\sf{\blue{\frac{x×11×9}{100×200}}}}$ = ${\sf{\blue{\frac{99x}{2}}}}$-----(2)

${\sf{\pink{Difference~in~intrest=412.50}}}$

${\sf{\blue{\frac{99x}{200}}}}$ - ${\sf{\blue{\frac{77x}{200}}}}$ = ${\sf{\blue{412.50}}}$

$\pink\implies$ ${\sf{\blue{\frac{99x}{200}}}}$ - ${\sf{\blue{\frac{77x}{200}}}}$ = ${\sf{\blue{\frac{41250}{100}}}}$

$\pink\implies$ ${\sf{\blue{\frac{99x-77x}{200}}}}$ = ${\sf{\blue{\frac{41250}{100}}}}$

$\pink\implies$ ${\sf{\blue{\frac{22x}{2}}}}$ = ${\sf{\blue{41250}}}$

$\pink\implies$ ${\sf{\blue{11x=3750}}}$

$\pink\implies$ ${\sf{\blue{x=41250}}}$

${\sf{\pink{Principal~amount=Rs.3750}}}$

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