Question

49. The price of oranges having been increased by 13% you have 4 oranges less for a
rupee.
How many oranges can now be had for a rupee?

Answer 1

A reduction of 33 1/3% in the price of oranges would enable a purchaser to obtain 8 more for a rupee. What was the price in paise, per orange, before the reduction?

Relation worth remembering :

If price reduced by 33 1/3% or 1/3, increase in quantity would be 1/(3 - 1) = 1/2 to keep expenditure constant.

=> If original quantity = Q then :

1/2 x Q = 8

=> Q = 16

Price per orange = 100/16 = 6.25 paise

:-)

Let x be number of oranges that can be bought with one rupee.

Then price of an orange is 1/x rs.

Now final price of orange becomes 2/(3x) rs.(as one third of price is reduced)

Then number of oranges now bought per rupee is 3x/2.

Thus extra oranges bought now is 3x/2-x=x/2.

Given x/2=8 =>x=16.

Thus price of each orange is 1/16 rupees or 6.25 paise before reduction of price.

Happy solving….

33 1/3=1/3

1 Rupee =100 paise

Let the rate of orange before reduction per piece be x paise

No. Of orange (s) that one can purchase

(1) (Before reduction )=100/x

New price of orange after reduction

x-x/3 =(2/3)x =2x/3 (paise )

Now no. of orange (s) one can purchase with 100 paise =100÷ (2x/3)=300/2x

According as the question

300/2x - 100/x=8

Or (300–200)/2x=8

Or 100/2x = 8

Or 16x = 100 or x =100/16 Or x = 6.25

Therefore price of orange /piece = 6.25 paise before reduction. (ANS )