Read the following information to answer the questions that follow :
The cost of fuming the engine of an army tank is proportional to the square of the speed and Rs 64 per hour for a speed of 16km/hr. Other costs amount to Rs 400 per hour. The tank has to make a journey of 400km at a constant speed.
Answer: D Cost =k* (speed)2 [where k is constant]
=> 64 = k*16*16
=> k = 1/4
Cost = (speed)2 /4
Total cost = cost of fuel* time + other cost* time
= (speed)2 /4 * distance/speed + 400*
distance/speed
Total cost = [(speed)2 /4 + 400] * 400/speed
using options, putting different values of speed, we find speed = 40km/hr to be most economical. Alternative: d(total cost)/d(speed) = 0
Given, v = 40km/hr.
Q. No. 2:
The total cost for the journey at this most economical speed is :
Answer: B Cost =k* (speed)2 [where k is constant]
=> 64 = k*16*16
=> k = 1/4
Cost = (speed)2 /4
Total cost = cost of fuel* time + other cost* time
= (speed)2 /4 * distance/speed + 400*
distance/speed
Total cost = [(speed)2 /4 + 400] * 400/speed
using options, putting different values of speed, we find speed = 40km/hr to be most economical. Alternative: d(total cost)/d(speed) = 0
Given, v = 40km/hr. Total cost = [(40)2 /4 + 400] * 400/40 = Rs 8,000.
Q. No. 50:
Sumant started a business investing Rs 48,000. After 6 months Maurya joined him with a capital of Rs 56,000. At the end of the year the total profit was Rs 24,529. What is the difference between the share of profits of Sumant and Maurya ?
Answer: A Sumant = 12* 48,000 Maurya = 6*56000 Sumant : Maurya = 12:7 Share of profit of Sumant = 12/19 * 24529 = 12* 1291 = Rs 15492. Share of profit of Maurya = Rs 9037. Difference between the share of profit of Sumant and Maurya => 15492 - 9037 = Rs 6455.
Q. No. 51:
A sum of money is divided among A,B,C and D in the ratio of 3:7:9:13 respectively. If the share of B is Rs 9180 more than the share of A, then what is the total amount of money of A and C together ?
Answer: A A,B,C and D in the ratio of 3:7:9:13 respectively A= 3x, B=7x, C=9x, D=13x. Difference between share of A and B = 4x 4x = 9180. Total money with A and C = 12 x = 3* 4x = 3* 9180 = Rs 27540.
Q. No. 52:
Rs 1950 is divided amongst three workers A, B and C such that 6 times of A's share is equal to 4 times B's share which is equal to 8 times C's share. How much did A get ?
Answer: A Let, A*6 = B*4 = C*8 = K A= K/6, B= K/4, C=K/8 Amount ratio among them = K/6 : K/4 : K/8 = 4:6:3 hence, A's share = [4/(4+6+3)] * 1950 = Rs 600.
Q. No. 53:
A,B and C enter into a partnership by investing Rs 28000, Rs 32000 and Rs 18000. A is working partner and gets a fourth of the profit for this services and the remaining profit is divided amongst the three in the ratio of their investments. What is the amount of profit that B gets if A gets a total of Rs 4995 ?
Answer: B Investment ratio among A,B and C = 28000 : 32000 : 18000 = 14:16:9 Suppose total profit = Rs x. A's profit for his service = Rs x * 1/4 = Rs x/4 remaining profit = x - x/4 = Rs 3x/4 A's profit according to his investment = Rs 3x/4 * 14/(14+16+9) = Rs 7x/26 Then, (x/4 + 7x/26) = Rs 4995 => (13x+14x)/52 = Rs 4995 => x = Rs 9620 Hence, B's profit = 3x/4 * 16/39 => (3*9620)/4 * 16/39 = Rs 2960.
Q. No. 54:
One year ago, the ratio between A's and B's salary was 4:5. The ratio of their individual salaries of last year and present year are 3:5 and 2:3 respectively. If their total salaries for the present year is Rs 6800, the present salary of A is
Answer: B Ratio of A's last year and present year salary = 3:5 Let salary be 3x and 5x respectively. Ratio of B's in last year and present year salary = 2:3 Let salary be 2y and 3y respectively. Given that, 3x/2y = 4/5 => 15x = 8y.............(i) Also, given that, 5x+3y = 6800............(ii) From equation (i) and (ii), we get y = 1200 and x = 640. A's present salary = 5x = 5*640 = 3200.