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In a mixture of syrup and water, there is 60 per cent syrup. If 5 litres of syrup is added then there is 35 per cent water in the mixture. The initial quantity of mixture was
  • a)
    40 litres
  • b)
    35 litres
  • c)
    30 litres
  • d)
    32 litres
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a mixture of syrup and water, there is 60 per cent syrup. If 5 litr...
Let the initial quantity of the mixture be x litres.
Syrup = .6x
Water = .4x
If 5 litres of syrup is added, syrup = .6x + 5
water = .4x
But .4x/x+5 = 35%
So, x = 35 litres
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Most Upvoted Answer
In a mixture of syrup and water, there is 60 per cent syrup. If 5 litr...
Solution:

Let the initial quantity of mixture be x litres.

Given, the mixture has 60% syrup. So, the remaining 40% is water.

Step 1: Before adding 5 litres of syrup

Syrup in the mixture = 60% of x litres = (60/100)x = 0.6x litres
Water in the mixture = 40% of x litres = (40/100)x = 0.4x litres

Step 2: After adding 5 litres of syrup

Total quantity of syrup in the mixture = 0.6x + 5 litres
Total quantity of water in the mixture = 0.4x litres

Given, after adding 5 litres of syrup, the mixture has 35% water. So, the remaining 65% is syrup.

Total quantity of mixture = (0.6x + 5) + 0.4x litres = 1x + 5 litres

Syrup in the mixture = 65% of (x + 5) litres = 0.65(x + 5) litres
Water in the mixture = 35% of (x + 5) litres = 0.35(x + 5) litres

We know that the total quantity of water in the mixture before and after adding 5 litres of syrup is the same.

Therefore, 0.4x = 0.35(x + 5)

0.4x = 0.35x + 1.75

0.05x = 1.75

x = 35

Therefore, the initial quantity of mixture was 35 litres.

Hence, option (b) is the correct answer.
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In a mixture of syrup and water, there is 60 per cent syrup. If 5 litres of syrup is added then there is 35 per cent water in the mixture. The initial quantity of mixture wasa)40 litresb)35 litresc)30 litresd)32 litresCorrect answer is option 'B'. Can you explain this answer?
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