There are five numbers ‘a’, ‘b’, ‘c’, ‘d’ and ‘e’. The average of ‘b’ and ‘c’ is 390. The value of ‘a’ is 40 more than 50% of ‘d’. The value of ‘e’ is 80 less than the value of ‘b’. The value of ‘d’ is 32 more than the 60% of ‘e’. The value of ‘c’ is 140 less than double the value of ‘e’.

As per the above given information, which of the following statements is/are correct?

(i) The value of ‘a’ is the multiple of 7.

(ii) The value of ‘d’ is completely divisible by 12.

(iii) 25% of ‘c’ is equal to 115.

Solution

The average of ‘b’ and ‘c’ is 390.

(b+c)/2 = 390

(b+c) = 780

b = (780-c)    Eq.(i)

The value of ‘e’ is 80 less than the value of ‘b’.

e = b-80

Put the value of ‘b’ from Eq.(i) in the above equation.

e = (780-c)-80

e = (700-c)    Eq.(ii)

The value of ‘c’ is 140 less than double the value of ‘e’.

c = 2e-140

Put the value of ‘e’ 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 ‘c’ in Eq.(ii).

e = (700-420)

e = 280

Put the value of ‘c’ in Eq.(i).

b = (780-420)

b = 360

The value of ‘d’ is 32 more than the 60% of ‘e’.

d = 32 + 60% of e

Put the value of ‘e’ in the above equation.

d = 32 + 60% of 280

d = 32 + 60% of 280

d = 32 + 168

d = 200

The value of ‘a’ is 40 more than 50% of ‘d’.

a = 50% of d + 40

Put the value of ‘d’ in the above equation.

a = 50% of 200 + 40

a = 100 + 40

a = 140

Now we have the values of ‘a’, ‘b’, ‘c’, ‘d’ and ‘e’.

(i) The value of ‘a’ is the multiple of 7.

The value of ‘a’ is 140 which is the multiple of 7. So the above given statement is correct.

(ii) The value of ‘d’ is completely divisible by 12.

The value of ‘d’ is 200 which is not completely divisible by 12. So the above given statement is not correct.

(iii) 25% of ‘c’ 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.