Q: Bhim has assembled a basket of fruit as a holiday gift for each of his friends- Santosh, Tarun, Ujjwal, and Varun. A total of fifteen pieces of fruits-five apples, five oranges and five pears are distributed among the four baskets according to the following conditions: Santosh , Tarun and Ujjwal will each receive exactly two different types of fruit. Varun will receive only apples. Tarun will receive more pieces of fruit than Santosh. Each basket includes at least three pieces of fruit. 1. If Varun’s basket contains more pieces of fruit than Tarun’s basket, then Tarun’s basket must contain:I. Four pieces of fruit.II. At least one orange.III. At least one pear. (a) I only (b) III only (c) Botha I and II (d) Both II and III 2. If Ujjwal’s basket contains more pieces of fruit than Tarun’s basket, all of the following must be false EXCEPT: (a) Only Varun will receive apple (b) Varun will receive exactly four apple. (c) Ujjwal will receive exactly two apple. (d) Tarun will receive exactly four pear.
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Explanation :
1. Answer (b) Santosh , Ujjwal and Varun must each receive at least three pieces, but Tarun must receive at least four pieces. The maximum number of pieces that any person may receive is six ( 6 + 3+ 3+3 = 15 ), and only Tarun may receive six pieces. Ujjwal and Varun each may receive as many as five pieces, while Santosh may receive only four pieces at maximum.At least one pear. 2. Answer (c) Varun may receive no more than five pieces and Tarun may receive no fewer than four pieces. As a result, if Varun receives more pieces than Tarun, then Varun must receive five pieces, and Tarun must receive four pieces. Thus, statement (a) must be true. Since Varun will receive five pieces, none of the other three friends will receive any apple, accordingly, each of the other three friends must receive at least one orange and at least one pear. Thus, statement (b) and (d) must be true.