A sum of ₹ 64 is made up of 80 coins which ar | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the number of $100$ paise coins be $x$ and the number of $50$ paise coins be $y$.We have $x + y = 80$ (Total number of coins).The total value

Vedclass · Accepted Answer

$32$

Vedclass · Answer

(B) Let the number of $100$ paise coins be $x$ and the number of $50$ paise coins be $y$.We have $x + y = 80$ (Total number of coins).The total value is $100x + 50y = 6400$ paise (Since ₹ $64 = 6400$ paise).Dividing the second equation by $50$,we get $2x + y = 128$.Subtracting the first equation from this,$(2x + y) - (x + y) = 128 - 80$,which gives $x = 48$.Substituting $x = 48$ into $x + y = 80$,we get $y = 80 - 48 = 32$.Alternatively,using the method of Alligation:Average value per coin $= \frac{6400}{80} = 80$ paise.Using the alligation rule:$100$ paise coins : $50$ paise coins $= (80 - 50) : (100 - 80) = 30 : 20 = 3 : 2$.Number of $50$ paise coins $= \frac{2}{3+2} 	imes 80 = \frac{2}{5} 	imes 80 = 32$.

$A$ sum of ₹ $64$ is made up of $80$ coins which are either $100$ $paise$ or $50$ $paise$ coins. How many coins are of $50$ $paise$?

Similar Questions

There are $3$ tubs which contain mixtures of milk and water in the ratios of $5:2, 4:3,$ and $3:1$ respectively. If the mixtures are poured into a single tub,find the ratio of milk to water.

In what ratio must water be added to spirit to gain $10 \%$ by selling it at the cost price?

$A$ sum of ₹ $390$ was divided among $450$ boys and girls. Each girl gets $50$ paise and each boy gets one rupee. How many girls are there among them?

Acid and water are mixed in a vessel $A$ in the ratio of $5:2$ and in the vessel $B$ in the ratio $8:5$. In what proportion should quantities be taken out from the two vessels so as to form a mixture in which the acid and water will be in the ratio of $9:4$?

$A$ person has ₹ $5000$. He invests a part of it at $3 \%$ per annum and the remainder at $8 \%$ per annum simple interest. His total income in $3$ years is ₹ $750$. Find the sum invested at different rates of interest (in ₹).

Vedclass Test Series

Exam Paper Generator

Online Exam Module