# A man buys postage stamps of denominations 25 paise and 50 paise for Rs. 10. He buys 28 stamps in total. Find the number of 25 paise stamps bought by him.$\left( a \right)$ 12$\left( b \right)$ 16$\left( c \right)$ 20$\left( d \right)$ 18

Verified
147.3k+ views
Hint: In this particular question assume any variable be the number of postage stamps of denominations 25 paise so the number of postage stamps of denominations 50 paise is (28 – x) as the total number of stamps he buys are 28, so use these concepts to reach the solution of the question.

Given data:
A man buys postage stamps of denominations 25 paise and 50 paise for Rs. 10.
Total number of postage stamps he buys are 28.
And the total amount he spent is Rs. 10
As we all know that 1 Rs = 100 paise.
So, 10 Rs. = 1000 paise.
Now, let the number of postage stamps of denominations 25 paise be X.
So the number of postage stamps of denominations 50 paise are (28 – X) as the total number of postage stamps are 28.
Now the sum of the multiplication of respective postage stamps with their respective cost is equal to the total amount he spent in paise.
So convert the above information into equation we have,
$\Rightarrow 25X + 50\left( {28 - X} \right) = 1000$
Now simplify this equation we have,
$\Rightarrow 25X + 1400 - 50X = 1000$
$\Rightarrow 25X = 1400 - 1000 = 400$
$\Rightarrow X = \dfrac{{400}}{{25}} = 16$
So there are 16 postage stamps of denominations 25 paise.
And the number of postage stamps of denominations 50 paise = (28 – X) = (28 – 16) = 12
So this is the required answer.
Hence option (b) is the correct answer.

Note: Whenever we face such types of questions the key concept we have to remember is that the sum of the multiplication of respective postage stamps with their respective cost is equal to the total amount he spent in paise, so construct the linear equation as above and simplify we will get the required number of postage stamps of 25 paise and 50 paise respectively.