500 g of jaggery syrup has 30% jaggery in it. The quantity of jaggery…

The correct answer is Option (1) → 200 g

The syrup has

    \(\text{jaggery} = 30\% \text{ of } 500 = 150\) g

Let x g of jaggery be added. Then the jaggery becomes \(150 + x\) and the syrup becomes \(500 + x\), and the jaggery must be half of the syrup:

    \( \displaystyle \frac{150 + x}{500 + x} = \frac{1}{2} \)

    \(300 + 2x = 500 + x\)

    \(x = 200\)

So 200 g of jaggery must be added.

Shortcut: Adding jaggery does not change the amount of water, which stays 500 − 150 = 350 g. In the new syrup the water is 50%, so the syrup weighs 700 g, and 700 − 500 = 200 g is added.