let 3 grandsons be g1, g2 & g3 resp'y given that g1+g2+g3 = y g2-g3 = x -------1) g1 = 2g2 2g2+g2+g3 =y ; so 3g2+g3 = y ----- 2) solving eq. 1 and 2 we get g2 = (x+y)/4 and g1= 2g2 so g1 = (x+y)/2 is the ans

for lion, lies on: mon tue wed so true on: thur fri sat sun. for rat, lies on: wed thur sat true on: mon tue fri sun.

so on TUESDAY the lion lies that it "did not lie yesterday" and its clear from the quest tat lion lies on tuesday and the previous day was monday which is one of the days the lion lies. rat says the truth tat "did not lie yesterday" and from question its clear tat rat speaks truth on tues and the sterday was monday which was one of the days for the rat tat it did not lied.

the series is a combination of two series... First one is 1, 3, 7, 15, 31, 63, ... (2^n - 1, n = 1, 2, 3, ...) Second one is 2, 7 (= 2 + 5), 22 (= 7 + 5*3), 67 (= 22 + 5*3*3), 202 ( = 67 + 5*3*3*3), ... Combining, we get 1, 2, 3, 7, 7, 22, 15, 67, 31, 202, 63, ... So, if it is number before 67, then it is 15 and if it is number after 67, then it is 31, followed by 202 and so on....

6 persons standing in queue with different age group, after two years their average age will be 43 and seventh person joined with them. hence the current average age has become 45. find the age of seventh person?

let age of 6 persons is 'x' after two years age will be =(x+12) average age=43 therefore (x+12)/6=43 ->x=246 (x+7th person age)/7= (246+7th person age)/7=45(average age) (by solving) the 7th person age is 69

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