ONE BANK LTD Special Cadre Officer -2017
WRITTEN MATH QUESTION SOLUTION
1. Length of a rectangular field is 1.5 times as large as its width. The field cost Tk 10260 for planting grass at 1.9TK per sq.meter. What will be the total cost of providing fence around the field that costs 2.5TK per meter?
Let the width of the rectangular field = x m and length = 1.5x m
According to the question
1.5x * x*1.9 = 10260
O r, x^2 = 3600
Therefore, x = 60
So, width = 60m, length = 90m
Perimeter = 2(60 + 90) = 350m
Cost = 350*2.5 = Tk750 (ans)
2. Salam used a part of TK 100,000 to purchase a TV of the remaining portion he invested 1/3 of it at 4% simple annual interest and 2.3 of it at 6% simple annual interest, If after a year the income from two investment totaled Tk 320. What was the purchase price of the TV?
Let, the purchase price of the TV = tk x
and remaining amount of money = tk(100,0 0 0 – x)
According to the question
(100,000 – x) * 1/3 *4% + ( 100,000 – x)*2/3 * 6% = 320
Or, 1000/3 * 4 + 12000/3 – 4x/300 – 12x/300 = 320
Or, 4000/3 + 12000/3 – 4x/300 – 12x/300 = 320
Or, 400000 + 1200000 - 4x – 12x = 320*300
Or, 16x = 1600000 – 96000
Or, 16x = 1504000
Or, x = 94,000(ans )
3. Solve the equation : 4/(2x+3) + 15/(5x+4) = 35/(7x+6)
4/( 2x+3) + 15/(5x+4) = 35/(7x+6)
Or, 4/(2x+3) + 15(5x+4) = 21/(7x+6) + 14/(7x+6)
Or, 4/(2x+3) - 14/(7x+6) = 21/(7x+6) – 15/(5x+4)
Or, (28x+24 - 28x - 42)/ (7x+6)( 2x+3) = (105x+84 - 105x - 90) / (5x+4)(7x+6)
Or, - 18/( 2x+3) = - 6/(5x+4)
Or, 9/(2x+3) = 3/(5x+4)
Or, 45x+36 = 6x+9
Or, 39x = - 27
Or, x = - 27/39 = - 9/13(ans)
4. A man has to go 10 km to catch a bus. He walks part of the way at 7 km/h and runs rest of the way at 12 km/h. If he takes 1 hr and 15 mins to complete his journey find the distance he covers by walking?
Let, he walks x km and run (10 – x) km
According to the question x/7 + (10 - x)/12 = 1hr 15mins
Or, (12x + 70 – 7x)/84 = 1+15/60
Or, 70 + 5x = 1.25*84 = 105
Or, 5x = 35
Or, x = 7 km (ans)