A farmer mixes three equal quantities of fertilisers. The first one contains 110 nitrogen, the second contains 950 nitrogen, and the third contains 360 nitrogen. What is the fraction of nitrogen in the mixture?
Step-by-step solution
To find: Fraction of nitrogen in the mixture
Idea: Fraction of nitrogen = nitrogen in the mixturequantity of the mixture. With equal quantities the q‘s cancel and the answer is the plain average of the three fractions.
- Nitrogen in the mixture = 110q + 950q + 360q = (0.1 + 0.18 + 0.05)q = 0.33q. (Note 360 = 120 = 0.05.)1 mark
- Fraction of nitrogen = 0.33q3q = 0.11 = 11100.1 mark
Check: With fractions: 110 + 950 + 120 = 10 + 18 + 5100 = 33100, and 33100 ÷ 3 = 11100 ✓. The answer lies between the smallest (0.05) and largest (0.18) ✓.
Answer to write in the exam
Let each quantity = q
Nitrogen = 110q + 950q + 120q = 10 + 18 + 5100q = 33100q
Fraction of nitrogen = 33q/1003q = 11100
∴ Fraction of nitrogen in the mixture = 11100
Common mistakes that cost marks
- Adding the fractions and stopping at 33100; that is the nitrogen in 3 quantities, so it must be divided by 3.
- Adding numerators and denominators: 1 + 9 + 310 + 50 + 60 = 13120. Fractions are added only after making the denominators equal.
- Misreading 360 as 0.5 instead of 0.05.
How this can come in the exam
Equal quantities of two mixtures containing 15 sugar and 310 sugar are mixed. The fraction of sugar in the mixture is
- 14
- 415
- 25
- 12
Show answer
(A) 14
12(210 + 310) = 12 × 510 = 14.
Try one yourself
Three equal quantities of mixtures with 14, 15 and 120 salt are mixed. Find the fraction of salt in the mixture.
Show answer
13(0.25 + 0.2 + 0.05) = 13 × 0.5 = 16.
More questions like this
- (Śrīdharācārya, Pāṭīgaṇita, c. 750 CE) In ancient India, Varṇa was the measure of gold purity. A purity of 16 varṇa meant pure gold; in general, a purity of k varṇa meant that the gold-alloy was k/16 gold and the rest impurities. (Now the term used is karat; 16 Varna = 24 karat.)
Suppose a goldsmith melts together three pieces of gold: 9 units at 12 varṇa, 5 units at 10 varṇa, and 17 units at 11 varṇa. Find the purity in varṇa of the combined gold. - The average rainfall per day in the months of May, June, and July in a certain location are 3.5 mm, 10 mm and 8.7 mm respectively. Write an expression that gives their combined average.
- Calculate the concentration of spice mix in these two scenarios.
- Rehmat’s marks in Maths are as follows: 60% in internal tests, 64% in the project, 73% in the final exam. The annual percentage score is calculated by combining the internals, project, and final exam in the ratio 3 : 2 : 5. What is Rehmat’s annual score in Maths?
- Savitri’s marks in Kashmiri are as follows: 35 out of 50 in internal tests, 44 out of 60 in the project, and 80 out of 100 in the final exam. The annual percentage score is calculated by combining the internals, project, and final exam in the ratio 3 : 4 : 5. Which of the following expression(s) gives her annual score (as a percentage) in Kashmiri?
(i) 35 × 3 + 44 × 4 + 80 × 53 + 4 + 5
(ii) (35/100) × 3 + (44/100) × 4 + (80/100) × 53 + 4 + 5
(iii) (35/50) × 3 + (44/60) × 4 + (80/100) × 53 + 4 + 5 × 100
(iv) ((35/50) × 100) × 3 + ((44/60) × 100) × 4 + ((80/100) × 100) × 53 + 4 + 5