Question
A reduction of 10% in the price of sugar enables a housewife to buy 6.2kg more for Rs279. Find reduced price per kilogram.
(a) Rs 5
(b) Rs 4.5
(c) Rs 4.05
(d) None of these
To solve this question we'll use the concept of Product constancy.
We know that the price and quantity are inversely proportional to each other therefore there product should always remain constant.
It is given that the price fall by 10%. i.e. new price will be (100-10)/100 of the older price.
=>price=9/10
To keep the product of quantity and price constant we need to increase the consumption to 10/9
=>quantity=10/9
=>(9+1)/9 i.e quantity is increased by 1/9 converting it to percent we've 100/9 i.e 11.11%.
Summary of above explanation :-
For two inversely proportional entity; decrease in one entity by 10% will require subsequent increase in other entity. This explanation can be extended to time and speed as well, since they also exhibit inverse relation. Click Here, for Product Constancy Table
Continuing with the solution :-
Since price and quantity are inversely proportional to each other we can say, 10% decrease in price will increase the consumption by 11.11% as explained above.
Now increase in 11.11%. i.e 11.11% = 100/9 % i.e. 1/9 of the original cost. But the increase in consumption is given as 6.2Kg .
Hence original consumption will be 6.2*9=55.8Kg
(increase is 1/9 so original will be 9 times 6.2)
Hence original price (cost per kg) will be = 279/55.8 = Rs 5
Hence reduced price (cost per kg) will be = 279/(55.8+6.2) = Rs 4.5
So correct answer is option (b)
Next Question (Ratio and Proportion) >> << Home
A reduction of 10% in the price of sugar enables a housewife to buy 6.2kg more for Rs279. Find reduced price per kilogram.
(a) Rs 5
(b) Rs 4.5
(c) Rs 4.05
(d) None of these
To solve this question we'll use the concept of Product constancy.
We know that the price and quantity are inversely proportional to each other therefore there product should always remain constant.
It is given that the price fall by 10%. i.e. new price will be (100-10)/100 of the older price.
=>price=9/10
To keep the product of quantity and price constant we need to increase the consumption to 10/9
=>quantity=10/9
=>(9+1)/9 i.e quantity is increased by 1/9 converting it to percent we've 100/9 i.e 11.11%.
Summary of above explanation :-
For two inversely proportional entity; decrease in one entity by 10% will require subsequent increase in other entity. This explanation can be extended to time and speed as well, since they also exhibit inverse relation. Click Here, for Product Constancy Table
Continuing with the solution :-
Since price and quantity are inversely proportional to each other we can say, 10% decrease in price will increase the consumption by 11.11% as explained above.
Now increase in 11.11%. i.e 11.11% = 100/9 % i.e. 1/9 of the original cost. But the increase in consumption is given as 6.2Kg .
Hence original consumption will be 6.2*9=55.8Kg
(increase is 1/9 so original will be 9 times 6.2)
Hence original price (cost per kg) will be = 279/55.8 = Rs 5
Hence reduced price (cost per kg) will be = 279/(55.8+6.2) = Rs 4.5
So correct answer is option (b)
Next Question (Ratio and Proportion) >> << Home
thanks dear
ReplyDeleteYe toh mera farz tha :D
DeleteReally?!
ReplyDeleteLet x be the original quantity.
Let x be the original price.
Now, Revised quantity = (x + 6.2)
Revised price = (1-0.1)y =0.9y
We know that price and quantity are inversely proportional. Hence,
xy = 0.9y * (x + 6.2)
=> xy = 0.9xy + 5.58y
=> 0.1xy = 5.58y
=> x = 55.8................(Cancelling y from both sides)
Hence, Original price = 279/55.8 = Rs 5
Revised price = 0.9 * 5 = Rs 4.5..............(Look at the expression for revised price)
That's a good approach. Thanks for your inputs !
ReplyDelete