Weight of A1 is six times of A2 and A2's weight is 50 percent more than that of A3. If the average weight of all three is 299 kgs, then what is the weight of A1?

Weight of A1 is six times of A2 and A2’s weight is 50 percent more than that of A3. If the average weight of all three is 299 kgs, then what is the weight of A1?

a) 1544 kg
b) 979 kg
c) 897 kg
d) 702 kg

Ans : d) 702 kg

SSC Constable GD Paper : Elementary Mathematics

Solution :

Let the weight of ( A_3 ) be ( x ).

According to the problem:

The weight of ( A_2 ) is 50% more than ( A_3 ), so:
A_2 = x + 0.5x = 1.5x
The weight of ( A_1 ) is six times the weight of ( A_2 ), so:
$A_1 = 6 \times A_2 = 6 \times 1.5x = 9x$

The average weight of ( A_1 ), ( A_2 ), and ( A_3 ) is given as 299 kg, so:
$\frac{A_1 + A_2 + A_3}{3} = 299$

Substitute the values of ( A_1 ), ( A_2 ), and ( A_3 ):
$\frac{9x + 1.5x + x}{3} = 299$
$\frac{11.5x}{3} = 299$
$11.5x = 299 \times 3 = 897$
Now, solve for ( x ):
$x = \frac{897}{11.5} = 78$