Question

A balloon-seller uses 2m of thread to tie for one balloon. If he has used 170698m of thread, the number of balloons sold by the seller is
[a] 85349
[b] 341396
[c] 0
[d] 2000

Answer 1

Hint: Assume that the total number of balloons sold by the balloon-seller be x. Hence find the total length of the thread used by the balloon-seller in terms of x. Equate this expression to 170698 and hence form an equation in x. Solve for x and hence find the total number of balloons sold by the balloon-seller.

Complete step-by-step answer:
Let the number of balloons sold by the balloon-seller be x.
Now, we know that for each balloon, the balloon seller uses a thread of length 2m.
Hence, we can write that the length of thread used by selling 1 balloon = 2m
Now, we can get the length of the thread used by selling x balloons by multiplying number and length as 2x.
This length of the total thread(in terms of x) should be equal to the total length of the thread used by the balloon-seller.
Since the total length of the thread used by the balloon-seller is 170698, we have
$2x=170698$
Dividing both sides by 2, we get
$x=\dfrac{170698}{2}=85349$
Hence the total number of balloons sold by the balloon-seller is 85349.
Hence option [a] is correct.

Note: Alternative solution: Using Unitary Method:
The number of balloons sold when the length of thread used is 2m is 1
Hence, the number of balloons sold when the length of the thread used is 1m is $\dfrac{1}{2}$
Hence the number of balloons sold when the length of the thread used is 170698 m is $\dfrac{170698}{2}=85349$, which is the same as obtained above. Hence option [a] is correct.