Theory Note, Formulas, Solution Note and Quiz of Algebra Exercise – 1 (C) Class 10th Odia
Linear simultaneous equations with two variables are an essential topic in Class 10 Mathematics. These equations appear in various real-life scenarios and mathematical problems, making them a powerful tool for solving different types of situations. Let’s explore some common applications of these equations.
ସରଳ ସହସମୀକରଣର ତୃତୀୟ Exercise -1(c) ରେ ଆମେ ସରଳସହସମୀକରଣର ପ୍ରୟୋଗ ବିଷୟରେ ଜାଣିବା। ବିଭିନ୍ନ ପାଟିଗଣିତର ସମାଧାନ ଆମେ ସରଳ ସହସମୀକରଣ ସାହାଯ୍ୟରେ କରିବା । କିଛି ଉଦାହରଣକୁ ଦେଖିବା
1. Age Problems
Age-related problems often involve comparing the ages of two individuals based on given conditions.
ବୟସ ସମ୍ବନ୍ଧୀୟ ପ୍ରଶ୍ନରେ ସାଧାରଣତଃ ଦୁଇଜଣଙ୍କର ବୟସ ଦିଅ ଯାଇ ଥାଏ ତ ସହିତ ଦୁଇଟି ତଥ୍ୟ ଦିଆ ଯାଇ ଥାଏ ଯାହାକୁ ବ୍ୟବହାର କରି ଆମେ ସମୀକରଣ ଗଠନ କରିବା ।
Example: A father is three times as old as his son. Five years ago, the father’s age was four times the son’s age. Find their present ages.
ଉଦାହରଣ: ପିତାଙ୍କ ବୟସ ପୁତ୍ର ବୟସର ତିନି ଗୁଣ। ପାଞ୍ଚ ବର୍ଷ ପୂର୍ବେ, ପିତାଙ୍କ ବୟସ ପୁତ୍ର ବୟସର ଚାରି ଗୁଣ ଥିଲା । ପିତା ପୁତ୍ରଙ୍କର ବର୍ତମାନର ବୟସ କେତେ
Solution: Let the father’s present age be x years and the son’s present age be y years.
- Given: x = 3y
- Five years ago: x-5 = 4(y-5)
- Solving these equations simultaneously gives the values of x and y.
2. Number Problems
Example: The sum of two numbers is 30, and their difference is 6. Find the numbers.
ଉଦାହରଣ : ଦୁଇଟି ସଂଖ୍ୟାର ସମଷ୍ଟି 30 ଏବଂ ତାଙ୍କର ବିୟୋଗଫଳ 6 ହେଲେ ସଂଖ୍ୟା ଦୁଇଟି କେତେ ।
Solution: Let the two numbers be x and y.
- Given: x+y = 30
- Also given: x-y = 6
- Solving these equations, we find the values of x and y.
3. Money and Coins Problems
Example: A person has ₹50 in the form of ₹5 and ₹10 notes. The total number of notes is 8. Find how many notes of each type the person has.
ଉଦାହରଣ : ଜଣେ ବ୍ୟକ୍ତିଙ୍କ ପାଖରେ 50 ଟଙ୍କା ଥିଲା 5 ଟଙ୍କିଆ ଓ 10 ଟଙ୍କିଆ ନୋଟରେ । ଯଦି ତାଙ୍କ ପାଖରେ ସର୍ବମୋଟ 8ଟି ନୋଟ ଅଛି ତାହେଲେ ତାଙ୍କ ପାଖରେ କେତୋଟି 5 ଟଙ୍କିଆ ଓ କେତୋଟି 10 ଟଙ୍କିଆ ନୋଟ ଅଛି
Solution: Let the number of ₹5 notes be x and the number of ₹10 notes be y.
- Given: x+y = 8
- Also given: 5x + 10y = 50
- Solving these equations gives values of x and y.
4. Work and Time Problems
Example: Two workers, A and B, together complete a task in 6 days. If A alone does it in 10 days, find how many days B alone would take to complete the work
ଉଦାହରଣ : ଦୁଇ ଜଣ ବ୍ୟକ୍ତି A ଓ B ଏକତ୍ର ଗୋଟିଏ କାମକୁ 6 ଦିନରେ ଶେଷ କରନ୍ତି । ଯଦି A ଏକ ସେହି କାମକୁ 10 ଦିନରେ ଶେଷ କରିଥାଏ, ତେବେ B ଏକାକି ସେହି କାମକୁ କେତେ ଦିନରେ ଶେଷ କରି ପାରିବ ।
Solution: Let A’s work per day be x and B’s work per day be y.
- Given: x + y = 1/6
- Also given: x = 1/10
- Solving these equations gives y, which helps find B’s time.
