MathematicsOne kilogram of tea and 4 kg of sugar together cost Rs.220. If the price of sugar increases by 50% and the price of tea increases by 10% the cost would be Rs.266. Find the original cost per kilogram of each.

One kilogram of tea and 4 kg of sugar together cost Rs.220. If the price of sugar increases by 50% and the price of tea increases by 10% the cost would be Rs.266. Find the original cost per kilogram of each.


  1. A
    Rs.60,Rs.40
  2. B
    Rs.60,Rs.30
  3. C
    Rs.60,Rs.20
  4. D
    Rs.20,Rs.40  

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    Solution:

    Given that 1 kg of tea and 4 kg of sugar together cost Rs. 220.
    If the price of sugar increases by 50% and price of tea increases by 10% the cost would be Rs. 266.
    Let the cost price of the tea and sugar be x and y respectively.
    Since, 1 kg of tea and 4 kg of sugar together cost Rs. 220, thus,
    ⇒x+4y=220……..(1)
    Since, the price of sugar increases by 50% and price of tea increases by 10% the cost would be Rs. 266. Thus,
    ⇒[x+(50100x)]+4y+(10100y)=266 ⇒32x+4(1110y)=266 ⇒32x+225y=266……………(2)
    Multiply equation (1) by 32 and then subtract equation by (2), we get,
    ⇒32x+6y-32x-225y=330-266 ⇒(30-225)y=64 ⇒85y=64 ⇒y=40 Substituting y=40 in equation (1),
    ⇒x+4(40)=220 ⇒x+160=220 ⇒x=60 Therefore, the cost prices of tea and sugar is Rs.60  and Rs.40 per kilogram, respectively.
    Hence the correct option is 1.
     
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