At a panipuri (golgappa) stall, the concentration of spice in the pani (spiced water) was 8%. Many customers complained that it was too spicy. What quantity of regular water should be mixed into the 10 litres of pani so that the spice level is reduced to (34)^th of the original concentration?

Step-by-step solution

Idea: Adding water does not change the amount of spice; it only increases the total volume. So set spicenew volume equal to the target concentration.

1. Target concentration = 34 × 8% = 6% = 0.06.½ mark
2. Spice in the pani = 8% of 10 L = 0.8 L. After adding x L of water the volume is (10 + x) L, with the same 0.8 L of spice.1 mark
3. 0.810 + x = 0.06 ⇒ 10 + x = 0.80.06 = 403 ⇒ x = 403 − 10 = 103.1 mark
4. So about 3.33 litres (313 L) of water must be added.½ mark

Check: 0.8 ÷ 13.33 = 0.06 = 6% ✓, and 6% is 34 of 8% ✓. A quicker view: to make the concentration 34, the volume must become 43 times, 10 × 43 = 1313 L.

Answer to write in the exam

Common mistakes that cost marks

• Reading ‘reduced to 34th’ as ‘reduced by 34‘, giving a target of 2% instead of 6%.
• Adding 2.5 L (a quarter of 10 L). Diluting to 34 needs the volume to grow to 43 of itself, which is 313 L more.
• Changing the amount of spice when water is added. Only the volume changes.

How this can come in the exam

Try one yourself

8 litres of pani contain 9% spice. How much water must be added to bring the spice level down to 6%?

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