A beaker contains 100 milligrams of a solution of salt and water that

(1st) Let the Amount of Water that we need to have Evaporate (in mg) = W

Question asks us to Solve for the Number of Hours it takes for the needed water to evaporate ----> Let this time = H


At a Rate of Y (mg per 1 hour) ------> the Water is Evaporating from the Solution

If we need W mg to evaporate in H hours at a Rate of Y (mg per 1 hour) ----> then:

H = W / Y

or

W = H * Y



(2nd)Originally we have (X)% Salt in 100 mg Solution --------> Water is going to Evaporate such that the New Solution will have (100 - W) mg and (X + 10)% Salt

NOTE: only Water is evaporating, so the Quantity of Salt that is in the Solution BEFORE = Quantity of Salt in the Solution AFTER the Water evaporates


Set up the Proportion:

(Amount of Salt) / (Total Amount of Solution - W mg of water that will evaporate) = (X + 10)%
*****************************************

Amount of Salt = (X)% * 100 mg

Total Amount of Solution = 100 mg

After W mg of Water Evaporates, the NEW Total Amount of Solution = (100 - W) mg
*****************************************


[ (X)% * 100 ] / [100 - W] = (X + 10)%


Finally, from above at (1st) ------> at Y mg per 1 hour for a Total of H hours, the Quantity of Water evaporating is:

W = Y * H ------> Substitute into Above equation


[ (X%) * 100 ] / [100 - YH] = (X + 10)% ——(this is the Equation we need to Manipulate and solve for H-hours)


(3rd) We need to Isolate H to answer the Question


[ (X%) * 100] / [100 - YH] = (X + 10)%

[ (X/100) * 100] / [100 - YH] = (X + 10) / (100)

[X] / [100 - YH] = (X + 10) / (100)

---Cross-Multiply-----

100X = (100 - YH) * (X + 10)

100X = 100X + 1,000 - XYH - 10YH


--Cancel 100X on Each Side and Group Like Terms and Factor Out H-----

XYH + 10YH = 1,000

H * (XY + 10Y) = 1,000

H = 1,000 / (XY + 10Y)


-D- is the Correct Answer

Total Solution (T1) = 100 mg
Salt(s1) = x % of Total Solution(100 mg) = x
Water(w1) = 100 - x

After evaporation, the salt content remains the same. But, now the salt constitutes (x +10) per cent of the solution.
x = (x+10)% of New total(T2) (This new total will be formed once the water is evaporated from solution)
New total (T2) = 100x /(x +10)

Composition of Water and Salt in New total:
Total Solution(T2) = 100x/(x+10)
Salt (S2) = x (Salt is not evaporated, the content will remain the same).
Water(W2) = New Total (T2) - Salt (S2) = 100x/(x+10) - x.

Now, we need to find the time that was needed for evaporation= Total Water Evaporated/ Rate of Evaporation.
Total Water Evaporated = Original Water (W1) - New Water(W2) = (100 - x) - [100x/(x+10) - x] = 1000/(x+10)
Rate of evaporation = y mg/hour.
Total Time = 1000/(x+10) divided by y = 1000/xy +10y.
Option D.