Question

Rahman bought $30$ stamps consisting of $20$ paise and $30$ paise stamps. Given that the stamps cost Rs.$7.80$ altogether, how many $20$ paise stamps did he buy?

• A. $12$
• B. $14$
• C. $16$
• D. $18$

Answer 1

The correct option is A $12$

Rahman bought $30$ stamps consisting of $20$ paise and $30$ paise stamps and total stamps cost Rs $7.80$.

Let $20$ paise stamps are $x$ and $30$ paise stamps are $y$

Then $x+y=30$ ............. $\left(i\right)$

Cost of $20$ paise stamps $=0.20x$

Cost of $30$ paise stamps $=0.30x$

But total cost of stamps is Rs $7.80$

Then, $0.20x+0.30y=7.80$ ............. $\left(ii\right)$

Multiply $\left(ii\right)$ by $10,$ we get

$0.20x\times 10+0.30y\times 10=7.80\times 10$

$2x+3y=78$ ............... $\left(iii\right)$

Also, from $\left(i\right)$

$3\times x+3\times y=3\times 30$

$\Rightarrow 3x+3y=90$.............. $\left(iv\right)$

Subtract $\left(iv\right)$ with $\left(iii\right)$, we get

$(3x+3y)-(2x+3y)=90-78$

$\Rightarrow 3x+3y-2x-3y=12$

$\Rightarrow x=12$

Then $20$ paise stamps are $12$.