In a famous Bel Air Apartments in Ranchi, there are three watchmen meant to protect the precious fruits in the campus. However, one day a theif got in without being noticed and stole some precious mangoes. On the way out however, he was confronted by the three watchmen, the first two of whom asked him to part with 1/3rd of the fruits and one more. The last asked him to part with 1/5th of the mangoes and 4 more. As a result he had no mangoes left. What was the number of mangoes he has stolen? the given answer is 15 pls explain in details with step.:-(
These types of questions generally should be solved by options which takes very less time. Anyways, suppose no of mangoes= x now first watchman takes=x/3+1=x+3/3 mangoes left=x-x+3/3=2x-3/3 second watchman takes=1/3 of rest+1 =2x-3/9+1=2x+6/9 mangoes left= 2x-3/3 - 2x+6/9 = 4x-15/9 third watchman takes= 1/5 of 4x-15/9 +4 now mangoes left finally=0 therefore, 4x-15/9 - (4x-15/45 +4) = 0 =>20x-75-4x+15-180/45=0 =>16x=240 =>x=15
In a famous Bel Air Apartments in Ranchi, there are three watchmen meant to protect the precious fruits in the campus. However, one day a theif got in without being noticed and stole some precious mangoes. On the way out however, he was confronted by the three watchmen, the first two of whom asked him to part with 1/3rd of the fruits and one more. The last asked him to part with 1/5th of the mangoes and 4 more. As a result he had no mangoes left. What was the number of mangoes he has stolen? the given answer is 15 pls explain in details with step.:-(
Yes, these kind of questions should be solved using options. As Rahicecream has explained the straight way, lets solve it using options and backtracking till we get the option.
See, he's left with 0. So b4 giving extra 4 mangoes to 3rd person he had 4/5*x=4 mangoes..Therfore,when he reached 3rd person he had x=5 mangoes. Similarly, before giving 1 extra mango to 2nd person he had (5+1extra mango=6)=> mangoes. Therefore after 1st person he had 2/3*x=6....x=9mangoes. Before 1st person:- 9+1extra mango=10mangoes which is 2/3 of mangoes left after giving 1/3 mangoes to 1st person. Therefore 2/3*x=10 gives x=15 as answer.
oh damn. i read the question as 1234....999 times. srry yaar.
here lets see. the number is something like. 12345678987654321.....999 times
forming pairs of 10 each -> 1234567898 7654321987 now both these pairs will complete their cycles of 50 each. but since there are 999 digits hence the last digit,ie, 7 wont be there. hence the number ends in 8. so completely divisible by 2. by 3; adding these pairs we get 105. 105*50 = 5250 - 7 = 5243 mod 3 = 2.
hence rem will be of the form 2k=3k+2.
tell me if theres something wrong.
The answer gotten as 5 is correct I believe.
You can't form pairs of 10 each and calculate the last digit.. :nono: the cycle isn't continuing... you are ending with 7 and starting with 1... ??? So, you have to form cycles of 17 digits.. 12345678987654321... and proceed...
1)two groups of students whose average age are 15 years and 25 years,combine to form a third group whose average is 23 years.What is the ratio of the number of students in the second group?
2)in an organisation,the daily average wages of 20 illiterate employees is decreased from Rs 25 to Rs 10.thus the average salary of all the literate and illiterate employees is decreased by Rs 10per day.the number of educated employees working in the organisation are:a)15 b)20 c)10 d)25
3)Mr.Akhilesh Bajpai while going from Lucknow to Jamshedpur covered half the distance by train at the speed of 96 km/hr, half the rest of the distance by his scooter at the speed of 40km/hr by car.the average speed at ehich he completed his journey is: a)64km/hr b)56 km/hr c)60km/hr d)36km/hr
4)Mr.Jaganmohan calculated the average of 10 ' three digit numbers'.but due to mistake he reveresed the digit of a number and thus his average increased by 29.7.the difference between the unit digit and hundreds digit of that number is: a)4 b)3 c)2 d)cant be determined
pls explain in detail with solution..i need the proceedings..thanks in advance..
Hi All, If anyone has any problem in any of the concepts of Number System. Just put it here Number System - Quantitative Aptitude racinghorror I will be glad to help you with your queries. Also, suggest in the comment section whatever other topics you want clarifications. Happy solving
1)two groups of students whose average age are 15 years and 25 years,combine to form a third group whose average is 23 years.What is the ratio of the number of students in the second group?
2)in an organisation,the daily average wages of 20 illiterate employees is decreased from Rs 25 to Rs 10.thus the average salary of all the literate and illiterate employees is decreased by Rs 10per day.the number of educated employees working in the organisation are:a)15 b)20 c)10 d)25
3)Mr.Akhilesh Bajpai while going from Lucknow to Jamshedpur covered half the distance by train at the speed of 96 km/hr, half the rest of the distance by his scooter at the speed of 40km/hr by car.the average speed at ehich he completed his journey is: a)64km/hr b)56 km/hr c)60km/hr d)36km/hr
4)Mr.Jaganmohan calculated the average of 10 ' three digit numbers'.but due to mistake he reveresed the digit of a number and thus his average increased by 29.7.the difference between the unit digit and hundreds digit of that number is: a)4 b)3 c)2 d)cant be determined
pls explain in detail with solution..i need the proceedings..thanks in advance..
1. Total 15 years = 15*x Total 25 years = 25*y => 15x + 25y / (x+y) = 23 => 15x + 25y = 23x + 23y => 8x = 2y => y/x = 4:1
2. Initial total wages of illiterate emp = 25*20 = 500 Total wages after deduction = 10*20 = 200 Difference = 500-200 = 300 i.e. rs. 300 got deducted from total wages of literate+illiterate employees. Now given, this decrease in total avegare is Rs.10 => Total employees = 300/10 = 30 => Literate emp = 30-20 = 10
3. Let the total distance be x km => Distance = Speed * time formula applied here => x / ( + ) => 2*96*40/(136) => Speed = 56km/hr on solving for x
4. Average of the numbers which are in correct order => (100a + 10b+ c) / 10 Average of the numbers which the number is reversed => (100c + 10b+ a) / 10 Given difference is 29.7 => 100c + 10b + a - 100a - 10b - c = 297 => 99c - 99a = 297 => c - a = 3
1)two groups of students whose average age are 15 years and 25 years,combine to form a third group whose average is 23 years.What is the ratio of the number of students in the second group?
2)in an organisation,the daily average wages of 20 illiterate employees is decreased from Rs 25 to Rs 10.thus the average salary of all the literate and illiterate employees is decreased by Rs 10per day.the number of educated employees working in the organisation are:a)15 b)20 c)10 d)25
3)Mr.Akhilesh Bajpai while going from Lucknow to Jamshedpur covered half the distance by train at the speed of 96 km/hr, half the rest of the distance by his scooter at the speed of 40km/hr by car.the average speed at ehich he completed his journey is: a)64km/hr b)56 km/hr c)60km/hr d)36km/hr
4)Mr.Jaganmohan calculated the average of 10 ' three digit numbers'.but due to mistake he reveresed the digit of a number and thus his average increased by 29.7.the difference between the unit digit and hundreds digit of that number is: a)4 b)3 c)2 d)cant be determined
pls explain in detail with solution..i need the proceedings..thanks in advance..
the soln is : 11 and 32 are coprime to each other => en(11) = 10 now 33^34 = 10k+9 =>32^33^34 =(10)^(10k+9) = (10)^9%11 (eulers theorem) =>rem = 10%11 = 10
a) The 444th term of the following sequence 1,2,3,10,11,12,13,20,21,22,23,30,31... is: (1) 1331 (2)17776 (3)12330 (4)13330
b) If P=abc and Q=uv are three digits and two digits two natural numbers respectively, such that u and v must be distinct integers. How many pairs of P and Q are there in total which give the same result when we multiply abc with uv as the product of cba with vu(positio of digits is interchanges): (1) 2 (2) 8 (3) 5 (4) can't be determined
(c) At his party, Praveen invited his 100 friends and they took their seats numbered 1,2,3,...100. starting from seat number 1 every third guest was served with chapatis and every fourth guest was served with poori and every fifth guest was served with dahi and the remaining guests were served coca-cola only. How many guests enjoyed coca cola? (1) 33 (2) 41 (c) 13 (d) cbd
This number system is killing me with such questions!
a) The 444th term of the following sequence 1,2,3,10,11,12,13,20,21,22,23,30,31... is: (1) 1331 (2)17776 (3)12330 (4)13330
b) If P=abc and Q=uv are three digits and two digits two natural numbers respectively, such that u and v must be distinct integers. How many pairs of P and Q are there in total which give the same result when we multiply abc with uv as the product of cba with vu(positio of digits is interchanges): (1) 2 (2) 8 (3) 5 (4) can't be determined
(c) At his party, Praveen invited his 100 friends and they took their seats numbered 1,2,3,...100. starting from seat number 1 every third guest was served with chapatis and every fourth guest was served with poori and every fifth guest was served with dahi and the remaining guests were served coca-cola only. How many guests enjoyed coca cola? (1) 33 (2) 41 (c) 13 (d) cbd
This number system is killing me with such questions!:-(
Qunit digit of 27!^37!? Q2 how many sets of values(x,y) satisfy 2x-5y=1;xcan u xpalin eulers remainder theorem with example?
First question 27! has unit digit zero, so raised to any power is obviously zero Second question: for odd values of y integral values of x can be obtained. First such values of x= 3,8,13....198 (ap with diff =5) all in all 40 such values of x, no restriction on y except positive hence answer should be 40......
a) The 444th term of the following sequence 1,2,3,10,11,12,13,20,21,22,23,30,31... is: (1) 1331 (2)17776 (3)12330 (4)13330
b) If P=abc and Q=uv are three digits and two digits two natural numbers respectively, such that u and v must be distinct integers. How many pairs of P and Q are there in total which give the same result when we multiply abc with uv as the product of cba with vu(positio of digits is interchanges): (1) 2 (2) 8 (3) 5 (4) can't be determined
(c) At his party, Praveen invited his 100 friends and they took their seats numbered 1,2,3,...100. starting from seat number 1 every third guest was served with chapatis and every fourth guest was served with poori and every fifth guest was served with dahi and the remaining guests were served coca-cola only. How many guests enjoyed coca cola? (1) 33 (2) 41 (c) 13 (d) cbd
This number system is killing me with such questions!:-(
Can somebody please explain how the last non zero digit no. of 25! in the above method is calculated. How have we arrived at 2^5*R(5)*R(0) and how is it coming out to be 2*2 ?
Answer to this will be 4*10^6.
25! has 6 zeros in the end ... (25=> 5+1 = 6) So, remainder by 10^7 will be last non zero digit of 25! follwoed by six 0s.
Last non-zero digit of 25! = 2^5 * R(5) *R(0) = 2 * 2 = 4
Note: R(n) i.e. last non-zero digit of n! can be found by putting n in the form of 5a+b. Then, R(n) = 2^a * R(a) * R(b)
It will be 67.
128^500 = 2^(7*500) = 2^3500
Now, 153 = 9*17. So, first let's find out remainder by 9 and 17.
Remainder by 9: 2^3 will leave remainder by 9 as 8 i.e. (-1). And 2^6 will leave remainder by 9 as 1. So, 2^3500 = 2^3498 * 2^4 = 2^6k * 2^2 will leave remainder as 1*4 = 4
Remainder by 17: 2^4 will leave remainder by 17 as 16 or (-1). So, 2^3500 = 2^(4*25*35) = (2^4)^(some odd number) = (-1)^(some odd number) = -1
So, we need to find a number of form, 9x+4 = 17y-1 => 67 at x=7 and y=4
Hi All, If anyone has any problem in any of the concepts of Number System. Just put it here Number System Quantitative Aptitude racinghorror I will be glad to help you with your queries. Also, suggest in the comment section whatever other topics you want clarifications. Happy solving
1st ans is 1:4,see x1+x2+ ...xn/n1=15..simillarly y1+y2+...yn/n2=25,,since boj the grp has jointed means....x1+....xn+y1+...+yn/n1+n2=23,,whch becames aftar solving 1:4..got it?
Qunit digit of 27!^37!? Q2 how many sets of values(x,y) satisfy 2x-5y=1;xcan u xpalin eulers remainder theorem with example?
unit digit will be 0 since in 27! Ast digit is 0 ... ..keep remember fr unit digit divid the power by 4 nd if u got a remander say x then we raise the power of base by x like .....22^42 so we hv remander 2 hence unit digt will be 2^2=4 ....
