This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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55) 'A' can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, 'A' alone can finish the remaining work? Step 1: Determine the daily work rate for A and B. A's daily work rate = (1)/(18) of the work per day. B's daily work rate = (1)/(15) of the work per day. Step 2: Calculate the amount of work B completed in 10 days. Work done by B = 10 days × (1)/(15) work/day = (10)/(15) = (2)/(3) of the work Step 3: Calculate the remaining work. Remaining work = Total work - Work done by B Remaining work = 1 - (2)/(3) = (1)/(3) of the work Step 4: Calculate the number of days A will take to finish the remaining work. Days for A = Remaining workA's daily work rate Days for A = (1)/(3)(1)/(18) = (1)/(3) × 18 = 6 days The correct option is C. C) 6 56) A sum of Rs. 12,500 amounts to Rs. 15,500 in four years at the rate of simple interest. What is the rate of interest? Step 1: Identify the principal amount (P), amount (A), and time (T). P = Rs. 12500 A = Rs. 15500 T = 4 years Step 2: Calculate the simple interest (I). I = A - P I = 15500 - 12500 = Rs. 3000 Step 3: Use the simple interest formula I = (P × R × T)/(100) to find the rate (R). 3000 = (12500 × R × 4)/(100) 3000 = 125 × R × 4 3000 = 500 × R Step 4: Solve for R. R = (3000)/(500) = 6 The rate of interest is 6%. The correct option is D. D) 6 57) The perimeter of the rectangle is 20 cm. If the length of the rectangle is 6cm, then its breadth will be Step 1: Write the formula for the perimeter of a rectangle. P = 2(l + b) Where P is perimeter, l is length, and b is breadth. Step 2: Substitute the given values into the formula. 20 cm = 2(6 cm + b) Step 3: Solve for b. (20)/(2) = 6 + b 10 = 6 + b b = 10 - 6 b = 4 cm The correct option is A. A) 4 cm 58) The simplest form of 15:25 is Step 1: Find the greatest common divisor (GCD) of 15 and 25. The factors of 15 are 1, 3, 5, 15. The factors of 25 are 1, 5, 25. The GCD is 5. Step 2: Divide both parts of the ratio by the GCD. 15 ÷ 5 = 3 25 ÷ 5 = 5 The simplest form of the ratio is 3:5. The correct option is D. D) 3:5