[নোটঃ এই আর্টিকেলটি (4) Decimals, Fraction, Percentage বিভাগের অধীনে 〈5〉Mixture and Coin Problems চ্যাপ্টারের অন্তর্গত, যা 〈4.5.a〉চিহ্ন দিয়ে প্রকাশ করা হয়েছে]
〈4.5.a〉বিভিন্ন ধরণের মিশ্রণ এবং মুদ্রা সম্পর্কিত সমস্যা
Chemical Mixtures
A [latex]500[latex] mL solution is [latex]20[latex]% alcohol by volume. If [latex]100[latex] mL of water is added, what is the new concentration of alcohol, as a percent of volume?
এ ধরণের অঙ্ক সমাধানের জন্যে mixture dilution সূত্র প্রয়োগ করতে হবে
Mixture dilution:
The concentration of a mixture may be expressed with percentage. The concentration always falls if water is added to this. We need to learn how this type of calculations is made:
[latex]C1V1=C2V2[latex]
Here,
[latex]C1[latex]= initial concentration
[latex]V1[latex]= initial volume
[latex]C2[latex]= final concentration
[latex]V2[latex]= final volume
Example:
Jack has [latex]3[latex] gallons of [latex]40[latex]% syrup preparation. How much water does he need to add there to make the concentration [latex]30[latex]%?
Solution: Here
[latex]C1=40[latex]%
[latex]V1=3[latex] gal
[latex]C2=30[latex]%
[latex]V2[latex] = ?
From the formula,[latex]{ V }_{ 2 }=\frac { ({ C }_{ 1 }{ V }_{ 1 }) }{ { C }_{ 2 } } [latex]
or, [latex]V2=(40[latex]%[latex]*3[latex]gal)/[latex]30[latex]%=[latex]4[latex]gal
So, he needs [latex](4-3)[latex]gal = [latex]1[latex]gal water. (Ans.)
Coin problems:
The key to these problems is to keep the quantity of coins distinct from the value of the coins. An example will illustrate.
Laura has [latex]20[latex] coins consisting of quarters and dimes. If she has a total of $[latex]3.05[latex], how many dimes does she have?
(A) 3
(B) 7
(C) 10
(D) 13
(E) 16
[Dime = 10 cent; Quarter = 25 cent]
Let [latex]D[latex] stand for the number of dimes, and let [latex]Q[latex] stand for the number of quarters. Since the total number of coins in 20, we get [latex]D+Q=20[latex], or [latex]Q=20-D[latex]. Now, each dime is worth [latex]10[latex]¢, so the value of the dimes is [latex]10[latex]D. Similarly, the value of the quarters is [latex]25[latex]Q = [latex]25(20-D[latex]). Summarizing this information in a table yields:
Notice that the total value entry in the table was converted from $[latex]3.05[latex] to [latex]30[latex]5¢. Adding up the value of the dimes and the quarters yields the following equation:
[latex]10D+25(20-D)=305[latex]
or, [latex]10D+500-25D=305[latex]
or, [latex]-15D=-95[latex]
so, [latex]D=13[latex]
Hence, there are [latex]13[latex] dimes, and the answer is ([latex]D[latex]).
