Ratio of the fares of First, Second and Third class category of a train between two stations is 10 : 7 : 2 and the ratio of passengers travelling in these category is 4 : 9 : 17 respectively. If the fare is increased by ¼ in First class, 1/8 in Second class and decreased by 10% in Third class and the ratio of number of passenger in these category remains same. If the new collection received is Rs. 60590, then find the total amount received from third class category.
Tell me the short approach to do the above...
Answers
Answer:
2407.86 approx
Step-by-step explanation:
Ratio of fares for I:II:III class = 10:7:2
So,
Fare for I class = 10x
Fare for IJ class = 7x
Fare for IJJ class = 2x
Ratio of passengers for I:II:III class =4:9:17
So,
Number of passengers in I class = 4y
Number of passengers in II class = 9y
Number of passengers in III class = 17y
Now,
In I class fare is increased by 1/4
So,
New fare for I class
= 10x + 10x/4
= (40x + 10x)/4
= 50x/4
= 25x/2
In II class fare is increased by 1/8
So,
New fare for II class
= 7x + 7x/8
= (56x + 7x)/8
= 63x/8
In III class fare is decreased by 10%
So,
New fare for III class
= 2x - 10% of 2x
= 2x - 2x*10/100
= 2x - x/5
= (10x - x)/5
= 9x/5
Here,
Total collection received by all categories is 60590.
So,
Collection by I class category + Collection by II class category + Collection by III class category = Total collection by all categories
4y*25x/2 + 9y*63x/8 + 17y*9x/5 = 60590
xy (4*25/2 + 9*63/8 + 17*9/5) = 60590
xy (50 + 567/8 + 153/5) = 60590
xy (2000 + 22680 + 6120)/40 = 60590
xy * 30800/40 = 60590
xy * 770 = 60590
xy = 60590/770 ........... (1)
Finally the collection for III class category
= 9x/5 * 17y
= 153xy/5
Putting value of xy by equation (1)
= 153*60590/5*770
= 927027/385
= 2407.86 approx