Maharashtra Board Class 9 Maths Chapter 6 Set 6.1 Algebra Standard Part 1 Financial Planning Solutions

Practice Set 6.1 Algebra 9th Standard Maths Part 1 Chapter 6 Financial Planning Solutions Maharashtra Board

Question 1. Alka spends 90% of the money that she receives every month, and saves Rs. 120. How much money does she get monthly?
Answer: Solution: Let Alka's monthly income be x. Alka spends 90% of the money that she receives every month.
Therefore, Amount spent by Alka = 90% of x
\( = \frac{90}{100} \times x = 0.9x \) Now, Savings = Income - Expenditure
Therefore, \( 120 = x - 0.9x \)
Therefore, \( 120 = 0.1 x \)
\( x = \frac{120}{0.1} = \frac{120 \times 10}{0.1 \times 10} \)
Therefore, \( x = 1200 \) Alka gets Rs. 1200 monthly.
In simple words: Alka saves Rs. 120, which is 10% (100%-90%) of her monthly income. By dividing her savings by the savings percentage, we find her total monthly income.

🎯 Exam Tip: Clearly identify what percentage of income is saved versus spent. This often simplifies the calculation by allowing direct proportion.

Question 2. Sumit borrowed a capital of Rs. 50,000 to start his food products business. In the first year he suffered a loss of 20%. He invested the remaining capital in a new sweets business and made a profit of 5%. How much was his profit or loss computed on his original capital ?
Answer: Solution: Original capital borrowed by Sumit = Rs. 50000 Sumit suffered a loss of 20% in his food products business.
Therefore, Loss suffered in the first year = 20% of 50000
\( = \frac{20}{100} \times 50000 \)
= Rs. 10000 Remaining capital = Original capital - loss suffered = 50000-10000 = Rs. 40000 Sumit invested the remaining capital i.e. 40,000 in a new sweets business. He made a profit of 5%. Profit in sweets business = 5% of 40000
\( = \frac{5}{100} \times 40000 \)
= Rs. 2000 New capital with Sumit after the profit in new sweets business = 40000 + 2000 = Rs. 42000 Since, the new capital is less than the original capital, we can conclude that Sumit suffered a loss. Total loss on original capital = Original capital - New capital = 50000 - 42000 = Rs. 8000 \[ \text{Percentage of loss} = \frac{\text{Total loss}}{\text{Original capital}} \times 100 \] \[ = \frac{8000}{50000} \times 100 \] = 16%
Therefore, Sumit suffered a loss of 16% on the original capital.
In simple words: Sumit initially lost 20% of his Rs. 50,000 capital, then gained 5% on the remaining amount. We calculate the net capital after these two transactions and compare it to the original capital to find the total loss percentage.

🎯 Exam Tip: Always compute percentages on the *current* capital amount at each stage of investment or loss, not always the initial capital unless specified.

Question 3. Nikhil spent 5% of his monthly income on his children's education, invested 14% in shares, deposited 3% in a bank and used 40% for his daily expenses. He was left with a balance of Rs. 19,000. What was his income that month?
Answer: Solution: Let the monthly income of Nikhil be x. Nikhil invested 14% in shares and deposited 3% in a bank.
Therefore, Total investment = (14% + 3%) of x = 17% of x
\( = \frac{17}{100} \times x \) = \( 0.17x \) Nikhil spent 5% on his children's education and used 40% for his daily expenses.
Therefore, Total expenditure = (5% + 40%) of x = 45% of x
\( = \frac{45}{100} \times x \) = \( 0.45x \) Amount left with Nikhil = 19,000 Amount left with Nikhil = Income - (Total investment + Total expenditure)
Therefore, \( 19000 = x - (0.17x + 0.45x) \)
Therefore, \( 19000 = x - 0.62x \)
Therefore, \( 19000 = 0.38x \)
\( x = \frac{19000}{0.38} = \frac{19000 \times 100}{0.38 \times 100} = \frac{1900000}{38} \)
\( = 50000 \)
Therefore, The monthly income of Nikhil is Rs. 50000.
In simple words: Nikhil's total spending and investments (17% + 45% = 62%) means 38% of his income is left. Since Rs. 19,000 is 38% of his income, his total income can be found by dividing Rs. 19,000 by 0.38.

🎯 Exam Tip: Sum up all percentage expenses and investments first. The remaining percentage will correspond to the leftover amount, allowing for a direct calculation of total income.

Question 4. Mr. Sayyad kept 40,000 in a bank at 8% compound interest for 2 years. Mr. Fernandes invested Rs. 1,20,000 in a mutual fund for 2 years. After 2 years, Mr. Fernandes got Rs. 1,92,000. Whose investment turned out to be more profitable?
Answer: Solution: Mr. Sayyad: Mr. Sayyad kept Rs. 40,000 in a bank at 8% compound interest for 2 years P = Rs. 40000, R = 8%, n = 2 years
Therefore, Compound interest (I) = Amount (A) - Principal (P) \[ =P \left(1+\frac{R}{100}\right) - P \] \[ P \left[1-\left(\frac{}{}+1\right)\right]^a= \] \[ = 40000 \left[\left(1+\frac{8}{100}\right)^2 -1\right] \] \[ = 40000 [(1 +0.08)^2 - 1] \] \[ = 40000 [(1.08)^2 - 1] \] \[ = 40000(1.1664 - 1) \] \[ = 40000 (0.1664) \] = Rs. 6656
Therefore, Mr. Sayyad's percentage of profit Interest \[ = \frac{\text{Interest}}{\text{Amount invested}} \times 100 \] \[ = \frac{6656}{40000} \times 100 \] = 16.64% ...(i) Mr. Fernandes: Amount invested by Mr. Fernandes in mutual fund = Rs. 120000 Amount received by Mr. Fernandes after 2 years = Rs. 192000
Therefore, Profit earned by Mr. Fernandes = Amount received - Amount invested = 192000-120000 = Rs. 72000
Therefore, Mr. Fernandes percentage of profit Profit earned \[ = \frac{\text{Profit earned}}{\text{Amount invested}} \times 100 \] \[ = \frac{72000}{120000} \times 100 \] = 60% From (i) and (ii), Investment of Mr. Fernandes turned out to be more profitable.
In simple words: We calculate the interest earned by Mr. Sayyad using the compound interest formula and express it as a percentage of his initial investment. For Mr. Fernandes, we find the absolute profit and express it as a percentage of his investment. Comparing the two percentages shows whose investment yielded a higher return.

🎯 Exam Tip: When comparing profitability, always convert absolute profits or interests into percentages relative to the initial investment to make a fair comparison.

Question 5. Sameera spent 90% of her income and donated 3% for socially useful causes. If she was left with Rs. 1750 at the end of the month, what was her actual income ?
Answer: Solution: Let the actual income of Sameera be x. Sameera spent 90% of her income and donated 3%.
Therefore, Sameera's total expenditure = (3% + 90%) of x = 93% of x
\( = \frac{93}{100} \times x \) = \( 0.93x \) Now, Savings = Income - Expenditure
Therefore, \( 1750 = x-0.93x \)
Therefore, \( 1750 = 0.07x \)
\( x = \frac{1750}{0.07} = \frac{1750 \times 100}{0.07 \times 100} = \frac{175000}{7} \)
\( = 25000 \)
Therefore, The actual income of Sameera is Rs. 25000.
In simple words: Sameera spent or donated a total of 93% of her income, meaning 7% of her income was left over. Since Rs. 1750 represents this 7%, her total income is Rs. 1750 divided by 0.07.

🎯 Exam Tip: Combine all percentage outgoings (spending, donations, investments) to find the total percentage of income utilized. The remaining percentage will directly relate to the saved or leftover amount.

Maharashtra Board Class 9 Maths Chapter 6 Financial Planning Practice Set 6.1 Intext Questions And Activities

Question 1. Amita invested some part of Rs. 35000 at 4% and the rest at 5% interest for one year. Altogether her gain was Rs. 1530. Find out the amounts she had invested at the two different rates. Write your answer in words. (Textbook pg. no. 97)
Answer: Solution: Let the amount invested at the rate of 4% and 5% be Rs. x and y respectively. According to the first condition, total amount invested = Rs. 35000
Therefore, \( x + y = 35000 \) ...(i) According to the second condition, total interest received at 4% and 5% is Rs. 1530.
Therefore, 4 % of x + 5 % of y = 1530
Therefore, \( \frac{4}{100} x + \frac{5}{100} y = 1530 \)
Therefore, \( 4x + 5y = 153000 \) ...(ii) Multiplying equation (i) by 4, we get
\( 4x + 4y = 140000 \) ...(iii) Subtracting equation (iii) from (ii), \[ \begin{aligned} 4x + 5y &= 153000 \\ 4x + 4y &= 140000 \\ \hline y &= 13000 \end{aligned} \] Substituting y = 13000 in equation (i),
\( x + 13000 = 35000 \)
Therefore, \( x = 35000 - 13000 = 22000 \)
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक निवेश समस्या का प्रतिनिधित्व करता है। यह दिखाता है कि एक कुल राशि (35000 रुपये) को दो अलग-अलग ब्याज दरों (4% और 5%) पर कैसे निवेश किया गया था। कुल निवेश की राशि को x + y = 35000 (i) के रूप में दर्शाया गया है, जबकि अर्जित कुल ब्याज को 4/100x + 5/100y = 1530 (ii) के रूप में दिखाया गया है। अंत में, यह x = 22000 और y = 13000 के रूप में प्रत्येक दर पर निवेश की गई अलग-अलग राशि को दर्शाता है।
Therefore, Amita invested 22000 at the rate of 4% and 13000 at the rate of 5%.
In simple words: Amita's total investment is Rs. 35,000, split between two interest rates (4% and 5%), earning a total of Rs. 1,530. We set up two linear equations representing the total investment and the total interest earned, then solve these equations simultaneously to find the individual amounts invested at each rate.

🎯 Exam Tip: For problems involving multiple investments with different rates, setting up a system of linear equations is crucial. One equation usually represents the total principal, and the other represents the total interest earned.