Question

A watch seller gained 20% by selling a watch for rupees 1260. what was its cost price and if we add gain 30% at what price should have it sold​

Answer 1

1365 rupees

Explanation:

1. Approach

The easiest method to solve this problem is via the method of proportions. One can use a proportion to find the original price of the watch. Then one can find the price of the watch if the watch had a (30%) mark up, by using a proportion.

2. Find the original price

Remember, the general format of a proportion is the following:

`(part)/(total)=(percent)/(100)`

The following information is given:

The watch sold for (1260) rupees which is (120%) of the original price. Remember, there was a (20%) gain, meaning that the seller recovered (120%) of the price, in essence, the price of the watch, plus (20%) extra, thus (120%). Substitute these values into the proportion and solve,

`(part)/(total)=(percent)/(100)`

`(1260)/(total)=(120)/(100)`

Simplify,

`(1260)/(total)=(120)/(100)`

`(1260)/(total)=(6)/(5)`

Cross product,

`(1260)/(total)=(6)/(5)`

`(5)(1260)=(6)(total)`

Simplify,

`(5)(1260)=(6)(total)`

`6300=6*total`

Inverse operations,

`6300=6*total`

`1050=total`

3. Find the price if the mark up is (30%)

Now, one knows the original price of the watch. Set up a proportion to find the price of the watch if there is a (30%) mark up. Use the same logic to set up this proportion as was used to set up the last one. The (percent) will be (130%) because the new price of the watch is (130%) of the original watch.

`(part)/(total)=(percent)/(100)`

Substitute,

`(part)/(total)=(percent)/(100)`

`(part)/(1050)=(130)/(100)`

Simplify,

`(part)/(1050)=(130)/(100)`

`(part)/(1050)=(13)/(10)`

Cross products,

`(part)/(1050)=(13)/(10)`

`(10)(part)=(13)(1050)`

Simplify,

`(10)(part)=(13)(1050)`

`10*part=13650`

Inverse operations,

`10*part=13650`

`part=1365`

Thus, the price after the (30%) is (1365) rupees.