Question
The average of four numbers (z+16), (y+15), (y-25) and
1.2z is (y-6). If one more number which is 144 is added then the new average will be (y-1). The value of ‘z’ is what percentage of the value of ‘y’?Solution
The average of four numbers (z+16), (y+15), (y-25) and 1.2z is (y-6).
(z+16)+(y+15)+(y-25)+1.2z = 4(y-6) Eq.(i)
If one more number which is 144 is added then the new average will be (y-1).
(z+16)+(y+15)+(y-25)+1.2z+144 = 5(y-1)
Put Eq.(i) in the above equation.
4(y-6)+144 = 5(y-1)
4y-24+144 = 5y-5
5y-4y = 144-24+5
y = 125
Put the value of ‘y’ in Eq.(i).
(z+16)+(125+15)+(125-25)+1.2z = 4(125-6)
(z+16)+140+100+1.2z = 4x119
(z+16)+140+100+1.2z = 476
256+2.2z = 476
2.2z = 476-256 = 220
z = 100
Required percentage = (100/125)x100
= (4/5)x100
= 80%
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