Question

Due to 25% increase in price of rice/kg a man able to purchase 20 kilograms less for Rs.400. what is the increase price of rice/kg.

Answer 1

Solution:-

Let original price of rice be Rs. 'x'  per kg
So, Toatl rice can be bought in Rs. 400 = 400/x (Kg)

After increase of 25 % in original price, the new price = x + (x*25)/100
= x + x/4
= 5x/4
So, quantity of rice can be bought after the price increase = 400*4/5x

Now, according to the question.
400/x - 20 = 1600/5x
2000 - 100x = 1600
100x = 2000 - 1600
x = 400/100
x = 4
The original price per kg of rice was Rs. 4
And the increased price is Rs. 4 + (4*25)/100
= 4 + 1 
Increased price per kg = Rs. 5

In Rs. 400 rice could be purchased at original price = 400/4 
= 100 kg
In Rs. 400 rice could be bought after increase of 25 % = 400/5
= 80 kg.
So, after increase of 25 % in per kg price of rice, 20 kg less rice could be purchased.

Answer 2

Solution -

Let us assume, x be the original price of rice and y be the original quantity of rice 

Given -

original price paid for the rice is

xy = 400 ---------------1

for 25% increase of price the man purchase 20 kilogram less for rs 400

Therefore,

1.25 x ( y- 20) = 400

1.25xy - 25x = 400   -------------2

Substitute the value of xy from equation 1

1.25 * 400 - 25x = 400

25x = 400 * 0.25

25x = 100

x = 4

Therefore, y = 400/x = 400/4 = 100

Answer - Original price of rice = Rs 4 per kg, so man purchased 100 kg.

After increase of 25%, man able to purchase 100 - 20 = 80 kg of rice

 price increase by  25% = 25/100 * 4 = 1

Therefore, increased price of rice = 4 + 1 = Rs 5. 

At Rs 5 per kg man able to purchase 80 kg rice.