Question
A factory has three belt conveyors fitted in its
loading station. Conveyors 'A' and 'B' operating simultaneously lift all the goods in the same time during which the goods can be lifted by the conveyor 'C' operating alone. Conveyor 'B' lifts all the goods five hours faster than conveyor 'A' but four hours slower than the conveyor 'C' The durations of time required to lift all the goods, individually by the conveyors 'A', 'B' and 'C' areSolution
Let conveyor B lifts all the goods in X hours. Conveyor A lifts all goods in X +5 Conveyor C lifts all goods in X – 4 hours. So, conveyor B takes 1/x time to lift in 1 hour Conveyor A takes 1/(x+5) hours to lift in 1 hour Conveyor C takes 1/(x-4) hours to lift in 1 hour. Now, according to the question, to lift all goods, Conveyor A + Conveyor B = Conveyor C 1/(x+5) + 1/x = 1/(x-4) Take LCM on the left side (x+5+x)/x(x+5)= 1/(x-4) 2x+5/x²+5x = 1/(x-4) (2x+5) *(x-4) = x² + 5x 2x²-8x+5x-20 = x² + 5x x²-8x-20 =0 x² - 10x + 2x - 20 = 0 x(x-10) + 2(x-10) = 0 (x-10)*(x+2) = 0 So, x= 10, -2 But x cannot be negative here. So, X = 10 Hence Conveyor B takes X 10 hours. Conveyor A take X + 5 = 10 +5 15 hours Conveyor C takes X-4 hours 10-4 = 6 hours Â
The ratio of cost price and selling price of a shirt is 7:8 respectively. The shirt was marked up by 25% above its cost price, and sold after giving Rs....
A shopkeeper purchases 22 dozen mangoes at a rate of Rs. 380 per dozen. He packages and sells them in boxes, each containing two dozen mangoes, for Rs. ...
Selling price of article ‘A’ when sold at a profit of 50% is Rs. 180 more than its selling price when sold at a loss of 40%. If the cost price of ar...
- A manufacturer earns a profit of 32% by selling a machine for Rs. 396. If he plans to make a profit of 48% while offering a discount of 20%, what should be...
- A bookseller made a profit of (100/9) % on selling a book. If he had purchased the book for 12.5% less than its original cost price and sold it for ₹6,24...
A person sold his goods after announcing two successive discounts of 32% each. The effective discount altogether is
- A shopkeeper cheats his customer by using faulty weight and earns profit percent of 12% after selling. How much less the shopkeeper will sell when the cust...
A, B, and C started a business with a total investment of Rs. 8000, distributed in the ratio 1:4:3. After five months, A added Rs. n to his initial inve...
A grocer sells wheat at a profit of 14% and uses a weight which is 24% less. Find his total percentage gain.
A school bag is sold for Rs.630 after giving two successive discounts of 20% and 30%. If school bag is marked up by Rs.600 above its cost price, then fi...
Relevant for Exams:
