Class 9 Mathematics Ganita Manjari Part 2 NCERT Solutions
Chapter-10: How Quantities Combine: Understanding Data
Exercise Set 10.3
1. A stationery shop owner made ₹8000 selling books, of which 30% is the profit amount, and ₹1000 selling book covers, of which 50% is the profit amount. What is the percentage of profit on the total sales?
Solution:
Total sales of books = ₹8000
Profit on books =30\% \ \text{of} \ ₹8000
= \frac{30}{100}\times 8000
= ₹2400
Total sales of book covers = ₹1000
Profit on books =50\% \ \text{of} \ ₹1000
= \frac{50}{100}\times 1000
= ₹500
Total profit = ₹2400+₹500=₹2900
Total sales = ₹8000+₹1000=₹9000
Profit percentage = \dfrac{\text{Total profit}}{\text{Total sales}}\times 100\%
= \dfrac{2900}{9000}\times 100\%
= \dfrac{290}{9}\%=32.22\%
2. The average daily distance travelled over 20 days is 44.5 km. On the 21st day, the stork flew 55 km. Find the average daily distance over all 21 days.
Solution:
Total distance in 20 days= 45.5 × 20 = 890 km
Total distance in 21 days= 890 + 55 = 945 km
New average = \dfrac{\text{Total distance in 21 days}}{\text{Number of days}}
= \dfrac{945}{21}= 45 km
3. A 600 mL solution containing 5% salt is mixed with a 300 mL solution containing 8% sugar. Find the concentrations of salt and sugar in the mixture.
(i) Salt: 5%, Sugar: 8% (ii) Salt: 13%, Sugar: 3%
(iii) Salt: 6%, Sugar: 6% (iv) Salt: 5.55%, Sugar: 8.88%
(v) Salt: 3.33%, Sugar: 2.67% (vi) Salt: 4.1%, Sugar: 7.08%
Solution:
Volume of the first solution = 600 mL
Amount of salt = \dfrac{5}{100}\times600=30 mL
Volume of the second solution = 300 mL
Amount of sugar = \dfrac{8}{100}\times300=24 mL
Total volume of mixture = 600 + 300 = 900 mL
Salt concentration in mixture = \dfrac{30}{900}\times100\%=3.33\%
Sugar concentration in mixture = \dfrac{24}{900}\times100\%=2.67\%
So, option (v) is correct.