Question

Cost of 3 balls $ = $ Cost of 2 pads. Cost of 3 pads $ = $ Cost of 2 gloves. Cost of 3 gloves $ = $ Cost of 2 bats. If the bat costs Rs.54, what is the cost of the ball?
A) Rs.12
B) Rs.14
C) Rs.16
D) Rs.18

Answer 1

Hint:
We can take the cost of each item as each variable. Then we can form linear equations with the given relations. Then we can use the given cost of bats to find the cost of gloves, then using it we can find the cost of pads and then cost of balls by making substitutions. Then the cost of the ball will be the required answer.

Complete step by step solution:
Let cost a ball be x, cost of a pad be y, cost of gloves be z and cost of bat be w.
It is given that the bat costs Rs.54.
 $ \Rightarrow w = 54$ … (1)
It given that, Cost of 3 gloves $ = $ Cost of 2 bats
 $ \Rightarrow 3z = 2w$
On substituting (1), we get,
 $ \Rightarrow 3z = 2 \times 54$
On dividing throughout with 3, we get,
 $ \Rightarrow z = \dfrac{{2 \times 54}}{3}$
On cancelling the common factors, we get,
 $ \Rightarrow z = 2 \times 18$
On simplification we get,
 $ \Rightarrow z = 36$ … (2)
Now it is given the Cost of 3 pads $ = $ Cost of 2 gloves.
 $ \Rightarrow 3y = 2z$
On substituting (2), we get,
 $ \Rightarrow 3y = 2 \times 36$
On dividing throughout with 3, we get,
 $ \Rightarrow y = \dfrac{{2 \times 36}}{3}$
On cancelling the common factors, we get,
 $ \Rightarrow y = 2 \times 12$
On simplification we get,
 $ \Rightarrow y = 24$ … (3)
Now it is given the Cost of 3 balls $ = $ Cost of 2 pads.
 $ \Rightarrow 3x = 2y$
On substituting (3), we get,
 $ \Rightarrow 3x = 2 \times 24$
On dividing throughout with 3, we get,
 $ \Rightarrow x = \dfrac{{2 \times 24}}{3}$
On cancelling the common factors, we get,
 $ \Rightarrow x = 2 \times 8$
On simplification we get,
 $ \Rightarrow x = 16$
Therefore, the cost of a ball is Rs. 16.

So, the correct answer is option C.

Note:
Alternate solution is given by,
Let cost a ball be x, cost of a pad be y, cost of gloves be z and cost of bat be w.
Now it is given the Cost of 3 balls $ = $ Cost of 2 pads.
 $ \Rightarrow 3x = 2y$
On dividing throughout with 3, we get,
 $ \Rightarrow x = \dfrac{{2 \times y}}{3}$ … (a)
Now it is given the Cost of 3 pads $ = $ Cost of 2 gloves.
 $ \Rightarrow 3y = 2z$
On dividing throughout with 3, we get,
 $ \Rightarrow y = \dfrac{{2 \times z}}{3}$ …. (b)
It given that, Cost of 3 gloves $ = $ Cost of 2 bats
 $ \Rightarrow 3z = 2w$
On dividing throughout with 3, we get,
 $ \Rightarrow z = \dfrac{{2 \times w}}{3}$ … (c)
Now we can substitute equation (b) in (a).
 $ \Rightarrow x = \dfrac{2}{3} \times \dfrac{{2 \times z}}{3}$
On simplification, we get,
 \[ \Rightarrow x = \dfrac{{4 \times z}}{9}\]
On substituting equation (c), we get,
 \[ \Rightarrow x = \dfrac{4}{9} \times \dfrac{{2 \times w}}{3}\]
On simplification, we get,
 \[ \Rightarrow x = \dfrac{{8 \times w}}{{27}}\] … (d)
It is given that the bat costs Rs.54.
 $ \Rightarrow w = 54$
On substituting this in equation (d), we get,
 \[ \Rightarrow x = \dfrac{{8 \times 54}}{{27}}\]
On simplification, we get,
 \[ \Rightarrow x = 8 \times 2\]
Hence, we have,
 \[ \Rightarrow x = 16\]
Therefore, the cost of a ball is Rs. 16.