Statement I, let the reward money received by Bob = $ R
The remaining money after spending $ 1000 of the total = R - 1000
The total simple interest received in 2 years 6 months = (R - 1000)*2.5*10/100 = 0.25R - 250 = 1000
Therefore, 0.25R = 1250
R = 5000 = the reward money received by Bob.
From the statement II,
let the reward money received by Bob = $ R
The remaining money after spending 25% of the total in travelling = 75% of R = 0.75R
20% of the remaining = 20% of 0.75 = 0.15R for bike
Remaining = 0.75R - 0.15R = 0.6R
The money left after gifting 2000 to his mom = 0.6R - 2000
The total money he received from the bank = 0.6R - 2000 + (0.6R - 2000)*2.5*10/100 = 0.6R - 2000 + 0.15R - 500 = 0.25R
0.5R = 2500
Therefore, R = 5000 = the reward money received by Bob.
Study Notes
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