Let after n week both tanks have same quantity of water .
for first tank
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tank hold 540 gallon of water ,
leaking of water 4 gallon /week
so, in n week water leak from the tank =4× n = 4n
now, after n week quantity of water in the tank = 540 -4n
for second tank
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quantity of water in the tank =720 gallon
leaking of water at the rate = 7gallon/week
so, after n week water leak from the tank = 7× n =7n
after n week quantity of water rest in the tank = 720 -7n
now ,
according to question ,
water in first tank = water in second tank
540 -4n = 720 -7n
7n -4n = 720 -540
3n = 180
n = 60
hence , after 60 week both tank have same quantity of water.
A geometric sequence is a sequence in which there is a common ratio between any two consecutive terms. In this case if X:Y:Z are in the ratio of 2:7:8 the multiplying by a constant k, we have X=2k, Y= 7k and Z=8k.
Then if X, Y-12, Z form a Geometric sequence, it means X/Y-12=Y-12/Z which is the same as 2k/7k-12=7k-12/8k if we cross multply, we get
16k²= 49k²-168k +144
33k²-168k+144 =0 solving for k
k = 4 or 1.091 if we take the whole number to find the values of X,Y and z,
X= 8, Y= 28 and Z=32
