The average of the present ages of A, B, C and D is (y-3) years. 12 years hence, the ratio between the ages of A and C is 9:8 respectively. The age of B is 6 years younger than D. The value of ‘y’ is the multiple of 12 but it should be less than 60. If the present age of D is 54 years, then which of the following is/are the possible values of ‘y’?
(i) 12
(ii) 24
(iii) 36
(iv) 48
If the present age of D is 54 years.
The age of B is 6 years younger than D.
present age of B = 54-6 = 48 years
The average of the present ages of A, B, C and D is (y-3) years.
Sum of the present ages of A, B, C and D = 4(y-3)
present age of A + present age of B + present age of C + present age of D = 4(y-3)
present age of A+48+present age of C+54 = 4(y-3)
12 years hence, the ratio between the ages of A and C is 9:8 respectively.
Let’s assume 12 years hence, the ages of A and C are ‘9a‘ and ‘8a‘ respectively.
(9a-12)+48+(8a-12)+54 = 4(y-3) Eq.(i)
(i) 12
Put the possible value of ‘y’ in Eq.(i).
(9a-12)+48+(8a-12)+54 = 4x(12-3)
(9a-12)+48+(8a-12)+54 = 4x9
17a+78 = 36
Here the value of ‘a’ will be negative. So this is not the possible value of ‘y’.
(ii) 24
Put the possible value of ‘y’ in Eq.(i).
(9a-12)+48+(8a-12)+54 = 4x(24-3)
17a+78 = 4x21
17a = 84-78 = 6
Here the value of ‘a’ will be in fractions. So this is not the possible value of ‘y’.
(iii) 36
Put the possible value of ‘y’ in Eq.(i).
(9a-12)+48+(8a-12)+54 = 4x(36-3)
17a+78 = 4x33
17a+78 = 132
17a = 132-78
17a = 54
Here the value of ‘a’ will be in fractions. So this is not the possible value of ‘y’.
(iv) 48
Put the possible value of ‘y’ in Eq.(i).
(9a-12)+48+(8a-12)+54 = 4x(48-3)
17a+78 = 4x45
17a+78 = 180
17a = 180-78
17a = 102
a = 6
Here the value of ‘a’ is a natural number. So this is the only possible value of ‘y’.
18.22 × 7.99 + 156.15 = ?
(91.004)2 - (40.003)2 - (52.9)2 = ?
?% of (128.31 ÷ 15.97 × 75.011) = 419.98
P spends 20% of his monthly income in travelling. He spends 25% of his monthly income on household expenses and spends 15% of his monthly income on fami...
25.22% of (59.9 × 8.01) + 69.97 =?
26.11 × 7.98 + 27.03 × 3.12 – 34.95 + 93.9 × 3.02 =?
30.11% of 149.99 + √195.97 ÷ 7.02 = ?
2280.03 ÷ 59.98 x 59.9 = ? + 30.32