A group of 74 students of Class XI went on picnic. The number of students who went on picnic by each section is as follows:Section A = 15Section B = 24Section C = 15Section D = 205 students from Section A spent as much as 4 students from Section B. 12 Section B students spent as much as 9 Section C students and 6 Section C students spent as much as 8 Section D student. If every student of a particular section spent the same amount and all the students spent Rs. 23,370 altogether, find the amount spent by each student of Section D?

Explanation:

GIVEN:A group of 74 students of CLASS XI went on picnic. The NUMBER of students who went on picnic by each section is as follows:Section A = 15Section B = 24Section C = 15Section D = 20Every student of a particular section spent the same amountAll the students spent Rs 23,370 altogetherSo, 15A + 24B + 15C + 20D = 23,3705 students from Section A spent as much as 4 students from Section B.So, 5A = 4B ---- (i)12 Section B students spent as much as 9 Section C students12B = 9C ---- (ii)6 Section C students spent as much as 8 Section D student6C = 8D ---- (iii)(i) + (ii) + (iii), we get:5A + 12B + 6C = 4B + 9C + 8D→ 5A + 8B – 3C – 8D = 0Multiplying the above equation by 3, we get:15A + 24B – 9C – 24D = 0On SUBTRACTING ‘15A + 24B – 9C – 24D = 0’ and ‘15A + 24B + 15C + 20D = 23,370’, we get:-24C – 44D = - 23,370Or, 24C + 44D = 23,370Again, 6C = 8D ---- (iii)Multiplying the above equation by 4, we get:24C = 32DNow, substituting the value of 24C in ‘24C + 44D = 23,370’, we get:32D + 44D = 23,370Or, 76D = 23,370Or, D = 307.5Hence, the amount spent by each student of Section D is Rs. 307.50.