# If the price of an article is reduced by 37.5%. A person can buy 6 more articles for Rs. 100. How many articles are available for Rs. 100 after reduct

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If the price of an article is reduced by 37.5%. A person can buy 6 more articles for Rs. 100. How many articles are available for Rs. 100 after reduction in price?
1. 10
2. 16
3. 4
4. 12

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Correct Answer - Option 2 : 16

GIVEN:

Reduction in price = 37.5%

Difference in the number of articles = 6

CONCEPT:

For the same amount of money,

Ratio of price and the ratio of consumption (number of articles) are inversely proportional.

Total cost = Price of one article × Total no. of articles

CALCULATION:

37.5% = 3/8

Original price = 8 units

Reduced price = 8 - 3 = 5 units

Original               Changed

Price -                8                          5

Articles -            5                          8

⇒ Difference in no. of articles = (8 - 5) = 3 units

3 units= 6

⇒ 8 units = 6 × (8/3) = 16 articles

∴ 16 articles are available for Rs. 100 after reduction.

ALTERNATE SOLUTION:

Let the original price be x and the original no. of articles be y.

Total cost is equal in both cases = Rs. 100

⇒  x × y = 5x/8 × (y + 6)

⇒ x × y = 5xy/8 + 15x/4

3xy/8 = 15x/4

y = 10

Number. of articles after reduction = 10 + 6 = 16

∴ 16 articles are available for Rs. 100 after reduction.