Question

A laboratory teacher had 1.5 litres of concentrated sulfuric acid. She replaces concentrated sulfuric acid with water after every class till the carton is empty. One student needs 10 ml of sulfuric acid mixture in every class. First class had 20 students and since then all other classes observed 10 students. Calculate total quantity of water with which mixture of sulfuric acid and water is replaced till carton is empty. Note 1.5 litres of concentrated sulfuric acid had 90% sulfuric acid and rest water

1. 7230 ml
2. 11230 ml
3. 10230 ml
4. 9230 ml
5. 8230 ml

Answer 1

Correct Answer - Option 4 : 9230 ml

Given:

Sulfuric acid with 90% concentration = 1.5 litres

First class = 20 students

One student = 10 ml of sulfuric acid mixture

Second class onwards = 10 students

Formula used:

Arithmetic progression: Tn = a + (n – 1) d

Sn = (a + L) × (n/ 2)

Calculation:

Class of 12 hence, amount of mixture replaced = 20 × 10

⇒ In first class amount of mixture replaced with water = 200 ml

Second class onwards only 10 students

⇒ from second class amount of mixture replaced = 100 ml

Arithmetic progression looks like:-

⇒ 200 + 300 + 400 + 500 + 600 + … + 1400 + 1500

⇒ Here, a = 200, d = 100, n = 13 (∵ the last 1500 ml would be pure water and hence it doesn’t need replacement)

⇒ 1400 = 200 + ((n – 1) × 100)

⇒ 1200 = (n – 1) × 100

⇒ n = 13

Total sum of replaced water,

⇒ S = (200 + 1400) × (13/ 2)

⇒ S = 9230 ml

∴ required total quantity of water for replacing mixture till carton is empty is 9230 ml