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Cost Price of Syrup per kg

CAT 2022 Slot 1 · Quantitative Ability · Hard · Profit and Loss

This is a hard Quantitative Ability question from the CAT 2022 Slot 1 paper. It tests Profit and Loss. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹ 308.32 per kg and makes an overall profit of 64%. Then, Amal's cost price for syrup, in rupees per kg, is

Answer

160

Explanation

Let Cost Price of juice per kg =5x= 5x. Then Cost Price of syrup per kg =4x= 4x.

Total Cost Price:

  • Syrup: 110×4x=440x110 \times 4x = 440x
  • Juice: 120×5x=600x120 \times 5x = 600x Total CP =1040x= 1040x.

Overall profit is 64%, so Total Selling Price (SP) =1040x×1.64=1705.6x= 1040x \times 1.64 = 1705.6x.

Individual Sales:

  1. 10 kg syrup at 10% profit: SP1=10×4x×1.1=44x\text{SP}_1 = 10 \times 4x \times 1.1 = 44x
  2. 20 kg juice at 20% profit: SP2=20×5x×1.2=120x\text{SP}_2 = 20 \times 5x \times 1.2 = 120x
  3. Remaining mixture: 100 kg syrup+100 kg juice=200 kg100\text{ kg syrup} + 100\text{ kg juice} = 200\text{ kg} sold at ₹ 308.32 per kg. SP3=200×308.32=61664\text{SP}_3 = 200 \times 308.32 = 61664.

Total SP =44x+120x+61664=164x+61664= 44x + 120x + 61664 = 164x + 61664.

Equating total SP: 1705.6x=164x+616641705.6x = 164x + 61664 1541.6x=616641541.6x = 61664 x=40x = 40

Cost price of syrup per kg =4x=4×40=160= 4x = 4 \times 40 = 160 rupees.

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