The first thing I did was to put the ratios into whole number form by multiplying both sides of a ratio by the same thing. This preserves the ratio, but makes the numbers a whole lot easier to work with.
This gives us a Jan M:F of 9:2 (multiplied by 6), and a Feb M:F of 1:3 (multiplied by 3/2).
The way that ratios work is that we know the proportion of males to females, but we don't know the totals. Since we don't know the totals, we can't compare the number of January female tourists to February female tourists yet.
For example, in January we could have had 9 male tourists and 2 females. We could have also had 900 male tourists and 200 females. So, what we know is that 9j + 2j = total January tourists, where j is the multiplier. In my first example (with 9 and 2) the multiplier was 1; in my second example, it was 100.
In the same way, we know 1f + 3f = total February tourists, where f is the ratio multiplier for February.
The problem tells us that " The no. of male tourists in JAN was 40% more thane the no. of female tourists in FEB." We know the male tourists in January can be represented by 9j, and the female tourists in Feburary by 3f. So, we can write this algebraically as:
9j = 1.4(3f)
j = 1.4*(3/9)*f
j=(1.4/3)*f
So now, we have a relationship between the ratio multipliers. We still don't know the total tourists, but this is enough to be able to compare the ratios in a meaningful way.
In January, we had 2j female tourists. Plugging in for j, we have 2*(1.4/3)*f. Thus, we had (2.8f/3) female tourists in January.
In February, we had 3f female tourists.
The formula for percentage change is 100*(new val - old val)/old val.
Plugging in, we have 100* (3f - (2.8f/3))/(2.8f/3). We can cancel out the f's in the numerator and demoninator, giving us:
100*(3 - (2.8/3))/(2.8/3). Since 3 = 9/3, the numerator is 6.2/3.
Now we have 100* (6.2/3)* (3/2.8) (multiplying by the inverse of a fraction is the same as dividing)
This reduces to 100*(6.2/2.8) = 221.43% (use whatever division technique works for you)
Thus, the answer is 1.
Last edited by
VP_Tatiana on Wed Jul 23, 2008 7:21 am, edited 1 time in total.
Tatiana Becker | GMAT Instructor | Veritas Prep
