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Let's denote the present age of the son as x. The man is 24 years older than his son, so the man's present age is x + 24. In two years, the son's age will be x + 2, and the man's age will be x...

Another method Let's count the numbers from 1 to 70 that have 1 or 9 in the unit's digit: Numbers with 1 in the unit's digit: 1, 11, 21, 31, 41, 51, 61 Numbers with 9 in the unit's digit:...

Let's denote the original number of apples as x. The fruit seller sells 40% of the apples, which means he sells 0.4x apples. The remaining apples are 60% of the original, which is 0.6x. Given...

Let's denote the marks obtained by the first student as x and the second student as y. Since one student secured 9 marks more than the other: x = y + 9 or y = x + 9 (we'll consider both cases)...

Let's denote the duration for which B joined the business as x months. A invests Rs. 85,000 for the entire year (12 months). B invests Rs. 42,500 for x months. The profit-sharing ratio is 3:1....

Let's denote B's contribution to the capital as x. A invests Rs. 3500 for the entire year (12 months). B invests x for 7 months (12 - 5). The profit-sharing ratio is 2:3. Since the profit...

Let me solve this step by step. 1) Let's understand the given information: * Profit ratio = 5 : 7 : 8 * Partner 1 invested for 14 months * Partner 2 invested for 8 months * Partner 3 invested for...

Let's denote the amount subscribed by C as x. Since B subscribes Rs. 5000 more than C: B's subscription = x + 5000 Since A subscribes Rs. 4000 more than B: A's subscription = (x + 5000) + 4000...

A's share of the profit is Rs. 855, and the ratio of A's investment to B's investment is 3:2. Let's denote the total profit as x. A's share of the profit is 3/5 of the remaining profit after 5%...

Cost Price (CP) of 26 kg rice = 26 × 20 = Rs. 520 CP of 30 kg rice = 30 × 36 = Rs. 1080 Total CP = 520 + 1080 = Rs. 1600 Total quantity of rice = 26 + 30 = 56 kg Selling Price (SP) of 56 kg rice...

Let's denote the Cost Price (CP) of the first transistor as x and the second transistor as y. For the first transistor: Selling Price (SP) = Rs. 840 Gain = 20% CP = x SP = CP + 20% of CP 840...

Cost Price (CP) of 100 oranges = Rs. 350 Selling Price (SP) of 1 dozen oranges = Rs. 48 SP of 100 oranges = 48 × (100/12) = 48 × 8.33 = 400 Since SP > CP, there is a profit. Profit...

Let's denote the Cost Price (CP) of the plot as x. Since the owner loses 15% when selling at Rs. 18,700: Loss = 15% of CP = 0.15x Selling Price (SP) = CP - Loss 18700 = x - 0.15x 18700 = 0.85x...

Let's denote the Cost Price (CP) of 1 ball as x. CP of 17 balls = 17x CP of 5 balls = 5x Given that the loss is equal to the CP of 5 balls: Loss = 5x Selling Price (SP) of 17 balls = Rs. 720 Since...

Cost Price (CP) of 6 articles = Rs. 5 CP of 1 article = 5/6 Selling Price (SP) of 5 articles = Rs. 6 SP of 1 article = 6/5 Profit = SP - CP = (6/5) - (5/6) = (36 - 25) / 30 = 11/30 Profit...

Let's denote the rate of interest as R. Simple Interest (SI) formula: SI = (P × R × Time) / 100 Compound Interest (CI) formula: CI = P × (1 + R/100)^Time - P Given values: P...

Simple Interest (SI) formula: SI = (P × R × Time) / 100 Given values: P = Rs. 1200 R = 10% per annum Time = 1 year SI = (1200 × 10 × 1) / 100 = 120 Compound Interest (CI) formula:...

Simple Interest (SI) formula: SI = (P × R × Time) / 100 Given values: SI = Rs. 50 R = 5% per annum Time = 2 years Rearrange the SI formula to solve for P: P = (SI × 100) / (R ×...

Simple Interest (SI) formula: SI = (P × R × Time) / 100 Given values: Borrowing: P = Rs. 5000 R = 4% per annum Time = 2 years SI (borrowing) = (5000 × 4 × 2) / 100 = (5000 × 8)...

Nominal rate of interest = 6% per annum Compounding frequency = Half-yearly (2 times a year) Effective annual rate of interest formula: Effective Rate = (1 + (R/n))^(n) - 1 where R = nominal...