Ronald can type = 32/6 page in 1 hour Elan can type = 40/5 page in 1 hour Thus they both can type = (32/6 + 40/5 ) pages in 1 hour = 40/3 Thus time taken to type 110 pages = 110/ (40/3) = 110*3/40 = 8.25 hours or 8 hours 15 minutes

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Note that,"We say that x varies as y, if x = ky for some constant k" Given ratio of prices of A, B and C = 2:3:4 Let their price be 2X, 3X and 4X respectively. Then D's price = 2X + 3X + 4X = 9X

Weight varies as square of price. Then A's weight = k 4X2 B's weight = k 9X2 C's weight = k 16X2 Sum of their weight = k 29X2 And D's weight = k 81X2

Therefore, k81X2 - k29X2 = 9880 kg k52X2 = 9880 KX2 = 190 Hence, D's weight = 81kX^2 = 81 x 190 = 15390 kg.

Let the number be X Two more than X = X + 2 Square of the number = (X + 2)2 Multiplied and divided by 2 and 5 = 2(X + 2)2 / 5 Twice the result is 500 = 2 x 2/5 x (X + 2)2 4/5 x (X + 2)2 = 500 (X + 2)2 = 500 x 5/4 (X + 2)2 = 625 X + 2 = 25 X = 23

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A B+C TW time 100 20 100 eff 1 5 condition is B = A+C B-C = A B-C = 1 B+C = 5 Solving these two we get B = 3 and C = 2 Time taken by C to complete the task = 100/2 = 50 days

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Green dyes =5 Blue dyes =4 Red dyes =3 The no of ways of choosing of at least one green and one blue is =(25?1)×(24?1)×23(25?1)×(24?1)×23 ?(32?1)×(16?1)×8?(32?1)×(16?1)×8 ?31×15×8?31×15×8 ?3720

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