Two pipes A and B would fill a cistern in 30 and 40 minutes respectively. Both pipes are opened.Determine the time the first pipe can be turned off so that the cistern may be just filled in 20 minutes?(a) After 10 minutes (b) After 15 minutes(c) After 20 minutes (d) After 22 minutes(e) After 25 minutes98. Mr. Avinash manufactures and sells a single product at a fixed price in a niche market. The sellingprice of each unit is ` 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2,where b and c are some constants. Avinash noticed that doubling the daily production from 20 to 40units increases the daily production cost by 66.66 percent. However, an increase in daily productionfrom 40 to 60 units results in an increase of only 50 percent in the daily production cost. Assume thatdemand is unlimited and that Avinash can sell as much as he can produce. His objective is tomaximize the profit. How many units should Mr. Avinash produce daily?(a) 70 (b) 100 (c) 130 (d) 150 (e) 18099. Two identical circles intersect so that their centres, and the points at which they intersect, form asquare of side 2 cm. What is the area of the portion that is common to both the circles?(a) 2( – 2) cm2 (b) 2( – 1) cm2(c) 2 cm2 (d) ( – 2) cm2(e) ( – 1) cm2100. What is the number of distinct terms in the expansion of 25x y z ?(a) 25 (b) 50 (c) 125 (d) 325 (e) 351101. There are five containers A, B, C, D and E each containing 1200 litres of water. The water is beingpumped from one tank to another as follows:From A to B at 30 litres/minuteFrom C to A at 60 litres/minuteFrom A to E at 20 litres/minuteFrom C to D at 50 litres/minuteFrom D to B at 80 litres/minuteFrom B to C at 60 litres/minuteFrom E to D at 10 litres/minuteFrom E to A at 10 litres/minuteWhich tank gets emptied first?(a) A (b) B (c) C (d) D (e) E102. In triangle DEF shown below, points A, B and C are taken on DE, DF and EF respectively such thatEC = AC and CF = BC. If angle D = 40 degress, then what is angle ACB in degrees?(a) 140 (b) 70 (c) 100 (d) 110 (e) 120103. Saga Internationals have conducted a chess competition between young boys and girls, wherein everyindividual has to play exactly one game with every other individual. It was found that in 66 games,both the players were girls, and in 210 games, both were boys. Find the number of games in which oneplayer was a boy and the other was a girl.(a) 210 (b) 222 (c) 252 (d) 276 (e) 290
Question
Two pipes A and B would fill a cistern in 30 and 40 minutes respectively. Both pipes are opened.Determine the time the first pipe can be turned off so that the cistern may be just filled in 20 minutes?(a) After 10 minutes (b) After 15 minutes(c) After 20 minutes (d) After 22 minutes(e) After 25 minutes98. Mr. Avinash manufactures and sells a single product at a fixed price in a niche market. The sellingprice of each unit is ` 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2,where b and c are some constants. Avinash noticed that doubling the daily production from 20 to 40units increases the daily production cost by 66.66 percent. However, an increase in daily productionfrom 40 to 60 units results in an increase of only 50 percent in the daily production cost. Assume thatdemand is unlimited and that Avinash can sell as much as he can produce. His objective is tomaximize the profit. How many units should Mr. Avinash produce daily?(a) 70 (b) 100 (c) 130 (d) 150 (e) 18099. Two identical circles intersect so that their centres, and the points at which they intersect, form asquare of side 2 cm. What is the area of the portion that is common to both the circles?(a) 2( – 2) cm2 (b) 2( – 1) cm2(c) 2 cm2 (d) ( – 2) cm2(e) ( – 1) cm2100. What is the number of distinct terms in the expansion of 25x y z ?(a) 25 (b) 50 (c) 125 (d) 325 (e) 351101. There are five containers A, B, C, D and E each containing 1200 litres of water. The water is beingpumped from one tank to another as follows:From A to B at 30 litres/minuteFrom C to A at 60 litres/minuteFrom A to E at 20 litres/minuteFrom C to D at 50 litres/minuteFrom D to B at 80 litres/minuteFrom B to C at 60 litres/minuteFrom E to D at 10 litres/minuteFrom E to A at 10 litres/minuteWhich tank gets emptied first?(a) A (b) B (c) C (d) D (e) E102. In triangle DEF shown below, points A, B and C are taken on DE, DF and EF respectively such thatEC = AC and CF = BC. If angle D = 40 degress, then what is angle ACB in degrees?(a) 140 (b) 70 (c) 100 (d) 110 (e) 120103. Saga Internationals have conducted a chess competition between young boys and girls, wherein everyindividual has to play exactly one game with every other individual. It was found that in 66 games,both the players were girls, and in 210 games, both were boys. Find the number of games in which oneplayer was a boy and the other was a girl.(a) 210 (b) 222 (c) 252 (d) 276 (e) 290
Solution
To determine the time the first pipe can be turned off so that the cistern may be just filled in 20 minutes, we need to calculate the rate at which each pipe fills the cistern.
Let's assume that the capacity of the cistern is 1 unit.
Pipe A fills the cistern in 30 minutes, so its rate of filling is 1/30 units per minute. Pipe B fills the cistern in 40 minutes, so its rate of filling is 1/40 units per minute.
When both pipes are opened, their combined rate of filling is (1/30 + 1/40) units per minute.
To find the time it takes to fill the cistern in 20 minutes, we can set up the equation:
(1/30 + 1/40) * t = 1
Simplifying the equation, we get:
(4/120 + 3/120) * t = 1 (7/120) * t = 1 t = 120/7
So, the time the first pipe can be turned off so that the cistern may be just filled in 20 minutes is approximately 17.14 minutes.
Therefore, the correct answer is not provided in the options given.
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