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Quadratic Equations

Long Answer Type

241. A chess board contains 64 equal squares and the area of each square is 6.25 cm². A border round the board is 2 cm wide. Find the length of the side of the chess board.

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242. Two pipes running together can fill a cistern in 6 minutes. If the pipe takes 5 minutes more than the other to fill cistern, find the time in which each pipe would fill the cistern.

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Short Answer Type

243. Two pipes running together can fill a cistern in

2 8 over 11 space minutes.

If one pipe takes 1 minute more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

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Long Answer Type

244. A pool is filled with three pipes with uniform flow. The first two pipes operating simul-taneously, fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool five hours faster than the first pipe and four hours slower than the third pipe. Find the time required by each pipe to fill the pool separately.

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Short Answer Type

245. A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

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246. Nimit takes 6 days less than the time taken by Tanvika to finish a piece of work. If both of them together finish the work in 4 days, find the time taken by Tanvika alone to finish the work.

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247. A takes 10 days less than the time taken by B to finish the a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

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248. In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English. The product of their marks, would have been 210. Find her marks in the two subjects.

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Long Answer Type

249. Out of number of Saras birds, one fourth the number are moving about in lotus plants; 1/9th coupled (along) with 1/4th as well as 7 times the square root of the number move on a hill; 56 birds remain in valcula trees. What is the total number of birds?

Solution not provided.
Ans. 576

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Short Answer Type

250. 250 apples were divided equally among a certain number of students. If there were 25 more students, each would have received half apple less. Find the number of students.

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