On selling a tea set at 5% loss and a lemon set at 15% gain, a crockery seller gains 7. If he sells the tea set at 5% gain and lemon set at 10% gain, he gains 13. Find the actual price of the tea set. If you travel by an autorickshaw, the fare for the first kilometre is different from the rate per km for the remaining distance. The total fare for a distance of 20 km is 37.70 and that for a distance of 26 Ian is 48.50. Find the auto fare for the first kilometre and for each successive kilomefre. One kilogram of tea and 4 kg of sugar together cost 220. If the price of sugar increases by 50% and the price of tea increases by 10%, the cost would be 266. Find the original cost per kilogram of each. If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder. Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and as remainder. Find the numbers.
Answers
Solution:-
Let the cost of tea set be Rs 'x' and the cost of lemon set be Rs 'y'.
The shopkeeper sells a tea set at 5 % loss and a lemon set ate 15 % gain.
So, the loss on tea set = x*5/100
And the gain on lemon set = y*15/100
Total gain = 15y/100 - 5x/100 = 70
15y - 5x = 7000
Dividing it by 5, we get
3y - x = 1400
-x + 3y = 1400...........(1)
If he sells the tea set at 5 % gain and lemon set at 10 % gain, he gains Rs 130.
Therefore,
5x/100 + 10y/100 = 130
5x + 10y = 13000
Dividing it by 5, we get
x + 2y = 2600 ..............(2)
Adding (1) and (2), we get
- x + 3y = 1400
x + 2y = 2600
______________
5y = 4000
______________
y = 4000/5
y = 800
Substituting the value of y = 800 in (2), we get
x + 2y = 2600
x + 2*800 = 2600
x + 2600 - 1600
x = 1000
So the cost price of tea set is Rs 1000 and the cost price of lemon set is Rs 800.
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