1. Find out the sum of all the numbers up to four digit made by 1, 2, 3 and 4 (repetition are allowed) E.g. 1+2+3+4+11+12+13+14+21+22+23+24+ …+4441+4442+4443+4444? (MARKS: 3/4/5)
2. A grass field of 120sq. meter bounded by a equilateral triangular compound. Three goats tied up with ropes that can just touch the opposite line. A goat can eat all grass which it only gets, half of that two can eat , and one third of that three can eat. How much a goat can eat? (Mark 2) ans.: onethird i.e. 40sq meter.
3. There are 100 bulbs and 100 switches. i. All bulbs are switched on. ii. All bulbs divided by two are switched on if off and switched off if on. iii. ,, ,, ,, ,, three –do iv. This continues upto 100 i.e. at last the bulb dived by 100 is switched on if off and off if on. How many bulbs wiil be in on condition after this? (Marks: 4/5)
5. When a boy is asked abt his age he said I’m 2.5 times the age of my sis now.Last yr.Iwas 3 times the age of hers.2 yrs. before Iwas 4 times her age .Before 3 yrs. I was7 times her age .Find out age of both. (Marks:4 )Ans:10, 4 Solution: 2.5x=y;3(x1)=y1;4(x2)=y2;7(x3)=y3; Boy(y)=10,Sis(x)=4.
6. In a apartment there are some families. i) No. of children > No.of Boys>No.of Girls>No.of families ii) Every family has children iii) A Girl has at least one Brother and at most one Sis iv) Children of one family > Sum (Children of all other families) Find out no. of families ,boys ,girls
7. Someone says to A,B,C,”I’ve a horse and his color is either Black,Brown,Grey.” A says it’s not Black B says it’s either Brown or Grey C says it’s Brown The person said among you one is correct and one is wrong . Find out the color of the horse .Ans:color is Grey;B is correct and C is wrong.Mark:2
8. There are 2 systems for temperature measurement A,B. System A System B 19 33 133 87 Find out the temp.when A=B.Ans.52.5 degree Soln:Take 2 consts.A,B. A+19B=33 and A+133B=87. Find Out A,B.Final eqn A+Bt=t.
9.A Sultan has 3 Queens Amina ,Fatin,Safie.Three thieves Abu,Kirsha,Badri stole 3 Jewels from these three Queens.Three jewels are Dimond ,Emerald,Ruby i) The Dimond thief is a bachelore and the dangerous among the three thieves. ii) Amina is younger to one who has Emerald. iii) Abu’s brother in law Kirsha is less dangerous than who take Emerald . iv) Badri has not stolen fromFatin(not sure sbt this stmnt) Who has which jewels and who theft which? Mark:8 Ans:Abu —Emerald(from Fatin) Kirsh—Ruby (from Amina) Badri—Dimond (from Safie)
10. There is a circle whose diameter is equal to the length of a chess board . If that is put on the chessboard how many complete squares will be in the circle. Ans.: It can be done both by calculation and graphical method. Answer is 32. Draw a square inside the circle. No: of square (area of inner square)/(area of single square of chess) 11. There is an idler and a devil. The devil said to the idler “cross the bridge and your money will be doubled. But you have to give 24$ to me every time you cross.” The idler did so. First time he crossed he find his money doubled and gave 24$ to the devil. He did so for the second time. When he crossed the bridge for the third time he found his total money equal to 24$ and has to give all to the devil. How much did he have at first? Ans.: 21$. Start from the last and go backward. 12. There is train moving at some speed (say x km/h). A person is also moving at some speed (2 km/h) towards certain direction either same as the train or opposite to that of the train. Find out how much time will it take for the train to cross the person? 13. Mathematician and children problem. Ans.: 6,6,1 years.
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