Ram added some water to the solution of juice and water such that the initial ratio a/b of juice to water gets inverted. Shyam sees Ram adding the water and he adds the juice to the solution such that the ratio of juice to water is back to its initial value. What is the possible value of ratio of amount of juice in the original solution to the final solution if both a and b are natural numbers?
A.1:5
B.5:7
C.3:2
D.4:9
Answers
Answer:
Step-by-step
1:5 and £:2
Answer:
Possible value of ratio of amount of juice in the original solution to the final solution is 4 : 9
Step-by-step explanation:
Scenario 1:
Initial ratio of Juice to water = a : b
Scenario 2:
Ram adds some water to juice solution. Now, the ratio of juice to water = a : c
It is given that the new ratio gets inverted in the second case.
So, a/c = b/a
c = a^2 / b
Therefore, ratio of juice to water = a : a^2 / b
Scenario 3:
Shyam adds some juice to the solution. Now the new ratio of juice to water = d : a^2 / b
It is given that the ratio becomes the initial value of a : b.
Therefore,
d/ a^2 / b = a / b
d = a^3 / b^2
Finally, the ratio of juice to water = a^3 / b^2 : a^2 / b
Ratio of juice in initial solution to final solution = a / (a^3 / b^2) = b^2 / a^2
Out of the given answer options, (d) 4 : 9 is the apt one, since it is only option with perfect square value of both numerator and denominator.