Question

A shopkeeper has just enough money to buy 52 cycles @ 525 per cycle. If each cycle were to cost 21 more, how many cycles can the shopkeeper now buy?
[a] 40
[b] 30
[c] 50
[d] 20

Answer 1

- Hint: Using the fact that the cost of one cycle is Rs 525 determines the cost of 52 cycles. Hence find the money the shopkeeper has. Assume that the total number of cycles he can now buy after the price hike of Rs 21 be n. Since he cannot buy more than n cycles, the cost of n+1 cycles, should be more than the money the shopkeeper has. Also, since he can buy n cycles, the cost of n cycles should be less or equal to the money the shopkeeper has. Hence find the range of n and hence find the value of n.

Complete step-by-step solution -
We have
The cost of one cycle = Rs 525
Hence the cost of 52 cycles $=52\times 525=27300$
Let the total number of cycles the shopkeeper can buy after the price hike be n.
New cost of one cycle =525+21 = 546
Since the shopkeeper can buy at least n cycles the cost of n cycles should be less or equal to the money the shopkeeper has. Hence, we have
$546n\le 27300$
Dividing both sides by 546, we get
$n\le 50$
Also, since the shopkeeper cannot buy n+1 cycles, the cost of n+1 cycles should be greater than the money the shopkeeper has.
Hence, we have
$546\left( n+1 \right)\ >\ 27300$
Dividing both sides by 546, we get
$\begin{align}
  & n+1\ >\ 50 \\
 & \Rightarrow n\ >\ 49 \\
\end{align}$
Hence, we have
$49\ \ <\ \ n\ \ \le 50$
Since n is natural number, we have
n =50
Hence the number of cycles the shopkeeper can now buy is 50
Hence option [c] is correct.

Note: Alternative Solution: In this method the chances of making a calculation mistake are less.
Let us assume that the shopkeeper can now buy 52-x cycles. For each cycle the shopkeeper has to spend extra 21 rupees. Hence in buying 52-x cycles, the shopkeeper would have to spend money equivalent to the earlier cost of x cycles.
Hence, we have
$\begin{align}
  & 21\left( 52-x \right)=525x \\
 & \Rightarrow 21\times 52-21x=525x \\
\end{align}$
Adding 21x on both sides, we get
$546x=21\times 52$
Dividing both sides by 546, we get
$x=\dfrac{21\times 52}{546}=2$
Hence the number of cycles the shopkeeper can now buy = 52-2 = 50, which is the same as obtained above.