The monthly income of a person was Rs. 3500 and his monthly expenditure was Rs. 9000. Next year, his income increased by 14% and his expenditure by 7%. Find the percentage increase... The monthly income of a person was Rs. 3500 and his monthly expenditure was Rs. 9000. Next year, his income increased by 14% and his expenditure by 7%. Find the percentage increase in his savings. In an election between two candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of voters enrolled in that election. A man's wage was reduced by 50%. Again the reduced wage was increased by 50%. Find his loss in terms of percentage. A television manufacturer earns 20% profit by selling each TV set for Rs. 14400. If the production cost is increased by 15%, what should be the new selling price of a set as to gain 15%? Five mangoes and four oranges cost as much as three mangoes and seven oranges. What is the ratio of the cost of one mango to the cost of one orange? Gautam started a business with a sum of Rs. 60000. Jatin joined him 8 months later with a sum of Rs. 35000. At what respective ratio will the two share the profit after two years? Read more

Steps to Solve

1. Problem Overview We need to address each question one by one, calculating the necessary values as required by each problem.

2. Question 45: Income and Savings Calculation

   • Monthly income = Rs. 3500
   • Monthly expenditure = Rs. 9000
   • Savings = Income - Expenditure = $3500 - 9000 = -5500$ (loss)
   • Next year, income increases by 14%: $$3500 \times 1.14 = 3990$$
   • Next year, expenditure increases by 7%: $$9000 \times 1.07 = 9630$$
   • Next year's savings = $3990 - 9630 = -5640$
   • Percentage increase in savings: $$\text{Percentage Change} = \frac{\text{New Savings} - \text{Old Savings}}{|\text{Old Savings}|} \times 100 = \frac{-5640 - (-5500)}{5500} \times 100$$
   • Calculate the percentage.

3. Question 46: Finding Total Votes

   • Let total votes be $x$.
   • Votes cast = 75% = $0.75x$.
   • Votes declared invalid = 2% of total = $0.02x$.
   • Valid votes = Total votes - Invalid votes = $x - 0.02x = 0.98x$.
   • Candidate votes = 9261, which is 75% of valid votes: $$9261 = 0.75(0.98x)$$
   • Solve for $x$.

4. Question 47: Percentage Loss Calculation

   • Initial wage = $w$.
   • Reduced wage = $0.5w$.
   • Increased wage after 50% = $0.5w \times 1.5 = 0.75w$.
   • Loss in terms of percentage: $$\text{Loss Percentage} = \frac{w - 0.75w}{w} \times 100$$
   • Simplify the expression to find the result.

5. Question 48: Selling Price Calculation

   • Cost price for T.V. = Rs. 14400 with 20% profit.
   • Selling price = Cost price + Profit = $14400 = x \times 1.20$.
   • Find $x$.
   • If production cost is increased by 15%, find new cost price: $$\text{New CP} = x \times 1.15$$
   • New Selling Price for gains of 15% on new cost price: $$\text{New Profit} = \text{New CP} \times 1.15$$

6. Question 49: Ratio Calculation

   • Cost of 5 mangoes = Cost of 3 mangoes + Cost of 7 oranges
   • Let cost of one mango be $m$ and one orange be $o$.
   • Set up an equation: $$5m = 3m + 7o$$
   • Rearrange to find the ratio of $m$ to $o$.

7. Question 50: Profit Sharing Ratio Calculation

   • Gautam's contribution = Rs. 60000, Jatin's contribution = Rs. 35000.
   • Jatin joined 8 months later, so Gautam's capital is considered for 24 months, Jatin's for 16 months.
   • Profit share ratio = (Gautam's investment) * (time) : (Jatin's investment) * (time): $$60000 \times 24 : 35000 \times 16$$
   • Simplify the ratio.