Question

A bag contains one rupee $50$ paise and $25$ paise coins in the ratio $5:6:8$. If the total amount is Rs.$420$, find the total number of coins.

• A. $798$
• B. $789$
• C. $978$
• D. $987$

Answer 1

The correct option is A $798$

$\Rightarrow$ The ratio of $Rs.1$, $50$ paise and $25$ paise coins is $5:6:8$

$\therefore$ Number of $Rs.1$ coins = $5x$.

$\Rightarrow$ Number of $50paise$ coins = $6x$

$\Rightarrow$ Number of $25paise$ coins = $8x$.

$\therefore$ Value of $5x$ $Rs.1$ coins = $Rs.1\times 5x=Rs.5x$.

$\Rightarrow$ Value of $6x$ $50paise$ coins = $6x\times 50paise=Rs.\frac{6x\times 50}{100}=Rs.3x$

$\Rightarrow$ Value of $8x$ $25paise$ coins = $8x\times 25paise=Rs.\frac{8\times 25}{100}=Rs.2x$

$\Rightarrow$ Total amount = $Rs.420$

$\therefore$ $5x+3x+2x=420$

$\therefore$ $10x=420$

$\therefore$ $x=\frac{420}{10}=42$

$\therefore$ Number of $Rs.1$ coins = $5\times 42=210$

$\therefore$ Number of $50paise$ coins = $6\times 42=252$

$\therefore$ Number of $25paise$ coins = $8\times 42=336$

$\Rightarrow$ Total number of coins = $210+252+336=798$