Question
There are five numbers βaβ, βbβ,
βcβ, βdβ and βeβ. The average of βbβ and βcβ is 390. The value of βaβ is 40 more than 50% of βdβ. The value of βeβ is 80 less than the value of βbβ. The value of βdβ is 32 more than the 60% of βeβ. The value of βcβ is 140 less than double the value of βeβ. As per the above given information, which of the following statements is/are correct? (i) The value of βaβ is the multiple of 7. (ii) The value of βdβ is completely divisible by 12. (iii) 25% of βcβ is equal to 115.Solution
The average of βbβ and βcβ is 390.
(b+c)/2 = 390
(b+c) = 780
b = (780-c)Β Β Eq.(i)
The value of βeβ is 80 less than the value of βbβ.
e = b-80
Put the value of βbβ from Eq.(i) in the above equation.
e = (780-c)-80
e = (700-c)Β Β Eq.(ii)
The value of βcβ is 140 less than double the value of βeβ.
c = 2e-140
Put the value of βeβ from Eq.(ii) in the above equation.
c = 2(700-c)-140
c = 1400-2c-140
c+2c = 1400-140
3c = 1260
c = 420
Put the value of βcβ in Eq.(ii).
e = (700-420)
e = 280
Put the value of βcβ in Eq.(i).
b = (780-420)
b = 360
The value of βdβ is 32 more than the 60% of βeβ.
d = 32 + 60% of e
Put the value of βeβ in the above equation.
d = 32 + 60% of 280
d = 32 + 60% of 280
d = 32 + 168
d = 200
The value of βaβ is 40 more than 50% of βdβ.
a = 50% of d + 40
Put the value of βdβ in the above equation.
a = 50% of 200 + 40
a = 100 + 40
a = 140
Now we have the values of βaβ, βbβ, βcβ, βdβ and βeβ.
(i) The value of βaβ is the multiple of 7.
The value of βaβ is 140 which is the multiple of 7. So the above given statement is correct.
(ii) The value of βdβ is completely divisible by 12.
The value of βdβ is 200 which is not completely divisible by 12. So the above given statement is not correct.
(iii) 25% of βcβ is equal to 115.
25% of c = 25% of 420 = 105
So the above given statement is not correct.
Thus we can say that only statement (i) is correct.
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