Question

Q1- On selling at set at 5% loss and a lemon at 15% gain a crockery seller gains Rs 7 . if he sells tea set at 5% gain and lemon set at 10% gain,he gains Rs 13.Find actual price of tea set and lemon set ?

Q2- Points A and B are 60 km apart from each other on a highway . A car starts from A and another from B at the same time. If they go in same direction , they meet in 9 hrs and if they go in opposite directions they meet in 9/7 hours. Find their speeds.

Answer 1

let    tea set costs:  T                lemon set costs:  L

then   gain =  - T * 5 /100  +  L * 15/100  =  Rs 7
        =>  15 L - 5 T = 700    --- (1)
 
 also    T * 5/100 + L * 10/100 =  Rs 13
       =>   10 L + 5 T =  1300    --- (2)

 add the equations to get:    L = Rs 80         and then  T = Rs 100
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   speed of A =  v1  kmph             
   speed of B = v2 kmph        let v2 > v1

if they travel in the same direction: 
         ( v2 - v1 ) * 9 hrs =  60 km
   =>   v2 - v1  = 20 / 3  kmph      ---- (1)

if they travel in opposite direction towards each other:
          (v1 + v2) * 9/7 hrs = 60  km
        =>  v1 + v2 =  140/3  kmph     --- (2)

     adding the two equations we get:    v2 =  80/3 kmph
                         v1 = 20 kmph