Practice Set 6.1 Algebra 9th Std Maths Part 1 Answers Chapter 6 Financial Planning
Question 1
Maharashtra Board Solution
Alka spends 90% of the money that she receives every month, and saves ₹ 120. How much money does she get monthly?
Solution & Step-by-Step Answer:
Let Alka’s monthly income be ₹ x. Alka spends 90% of the money that she receives every month. ∴ Amount spent by Alka = 90% of x = × x = 0.9x 100 Now, Savings = Income – Expenditure ∴ 120 = x – 0.9x ∴120 = 0.1 x ∴ ∴ x = 1200 Alka gets ₹ 1200 monthly.
Question 2
Maharashtra Board Solution
Sumit borrowed a capital of ₹ 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 ?
Solution & Step-by-Step Answer:
Original capital borrowed by Sumit = ₹ 50000 Sumit suffered a loss of 20% in his food products business. ∴ Loss suffered in the first year = 20% of 50000 = × 50000 = ₹10000 Remaining capital = Original capital – loss suffered = 50000- 10000 = ₹ 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 = x 40000 100 = ₹ 2000 New capital with Sumit after the profit in new sweets business = 40000 + 2000 = ₹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 = ₹ 8000 ∴ Sumit suffered a loss of 16% on the original capital.
Question 3
Maharashtra Board Solution
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 ₹ 19,000. What was his income that month?
Solution & Step-by-Step Answer:
Let the monthly income of Nikhil be ₹ x. Nikhil invested 14% in shares and deposited 3% in a bank. ∴ Total investment = (14% + 3%) of x = 17% of x = × x = 0.1 7 x Nikhil spent 5% on his children’s education and used 40% for his daily expenses.
∴ Total expenditure = (5% + 40%) of x
= 45% of x
= × x
= 0.45x
Amount left with Nikhil = 19,000
Amount left with Nikhil = Income – (Total investment + Total expenditure)
∴ 19000 = x – (0.17x + 0.45x)
∴ 19000 = x – 0.62x,
∴ 19000 = 0.38x
∴
= 50000
∴ The monthly income of Nikhil is ₹ 50000.
Question 4
Maharashtra Board Solution
Mr. Sayyad kept ₹ 40,000 in a bank at 8% compound interest for 2 years. Mr. Fernandes invested ₹ 1,20,000 in a mutual fund for 2 years. After 2 years, Mr. Fernandes got ₹ 1,92,000. Whose investment turned out to be more profitable?
Solution & Step-by-Step Answer:
Mr. Sayyad: Mr. Sayyad kept ₹ 40,000 in a bank at 8% compound interest for 2 years P = ₹ 40000, R = 8%, n = 2 years ∴ Compound interest (I) = Amount (A) – Principal (P) = 40000 [(1 +0.08)2 – 1] = 40000 [(1.08)2 – 1] = 40000(1.1664 – 1) = 40000 (0.1664) = ₹ 6656 ∴ Mr. Sayyad’s percentage of profit Interest
Mr. Fernandes:
Amount invested by Mr. Fernandes in mutual fund = ₹ 120000
Amount received by Mr. Fernandes after 2 years = ₹ 192000
∴ Profit earned by Mr. Fernandes
= Amount received – Amount invested
= 192000- 120000
= ₹72000
∴ Mr. Fernandes percentage of profit Profit earned
= 60%
From (i) and (ii),
Investment of Mr. Fernandes turned out to be more profitable.
Question 5
Maharashtra Board Solution
Sameera spent 90% of her income and donated 3% for socially useful causes. If she was left with ₹ 1750 at the end of the month, what was her actual income ?
Solution & Step-by-Step Answer:
Let the actual income of Sameera be ₹ x. Sameera spent 90% of her income and donated 3%. ∴ Sameera’s total expenditure = (3% + 90%) of x = 93% of x = × x = 0.93x Now, Savings = Income – Expenditure ∴ 1750 = x-0.93x ∴ 1750 = 0.07x ∴ The actual income of Sameera is ₹ 25000.
Maharashtra Board Class 9 Maths Chapter 6 Financial Planning Practice Set 6.1 Intext Questions and Activities
Question 1
Maharashtra Board Solution
Amita invested some part of ₹ 35000 at 4% and the rest at 5% interest for one year. Altogether her gain was ₹ 1530. Find out the amounts she had invested at the two different rates. Write your answer in words. (Textbook pg. no. 97)
Solution & Step-by-Step Answer:
Let the amount invested at the rate of 4% and 5% be ₹ x and ₹ y respectively. According to the first condition, total amount invested = ₹ 35000 ∴ x + y = 35000 …(i) According to the second condition, total interest received at 4% and 5% is ₹ 1530. ∴ 4 % of x + 5 % of y = 1530 ∴ x x + x y = 1530 ∴ 4x + 5y = 153000 …(ii) Multiplying equation (i) by 4, we get 4x + 4y = 140000 …(iii) Subtracting equation (iii) from (ii), Substituting y = 13000 in equation (i), x + 13000 = 35000 ∴ x = 35000 – 13000 = 22000 ∴ Amita invested ₹ 22000 at the rate of 4% and ₹ 13000 at the rate of 5%.