Question

The least number which when divided by 48,64,90,120 leave the remainders 38,54,80,110 respectively is

Answer 1

The first solid hint here is that the remainder when divided by 120 is 110. That means whatever it is, it is divisible by 10. I'm checking mentally to see if guess-and-check is an efficient way to solve this.

Answer 2

Oh, note that 48*5=240=120*2 In fact, most of these numbers have only a few prime factors different from each other.

Answer 3

ho we can solve this typpe of ques fast

Answer 4

can u plz explain me properly

Answer 5

Note the similarities in the numbers. 90*8=720=120*6=48*15 All remainders are 10 less than the number, so we now know that this is 10 less than a multiple of 720

Answer 6

That just leaves 64, which, come to think of it, also leaves a remainder 10 less than itself.

Answer 7

64*45=2880=720*4. We now have a number with all of these factors in common. There is, of course, a faster way!

Answer 8

is there any simple way to solve such problems?

Answer 9

Once you've noticed that each remainder is 10 less than the number itself, factor each number before you start multiplying.

Answer 10

can u plz show by this quest the fast method?

Answer 11

OK. 48, 64, 90, and 120 leave remainders of 38, 54, 80, and 110. Each remainder is 10 less than the original number. This means our final number must be the Least Common Multiple (LCM) of these four numbers minus ten.

Answer 12

got the ans
2870..is it right?
I took the LCM of 48,64,90,120 & then less 10 from it

Answer 13

\[ 48=2^4*3^1. 64=2^6. 90=2^1*3^2*5^1. 120= 2^3*3^1*5^1.\]
Take the highest power of each prime factor, then multiply them: \[2^6 from64, 3^2 from90, and 5^1 from 90 or 120\]
\[ 2^6*3^2*5^1=2880 \]
That means you're right!

Answer 14

thankyou

Answer 15

A,B,C subscribs together Rs 50,000 in a business.A subscribes 4000 more than B,B subscribes 5000more than C.Out of the toal profit of 35000,A recieves?

Answer 16

A=C+9,000
B=C+5,000
Total=50,000=A+B+C=14,000+3C
Solve for A, B, and C, then take that ratio and apply it to 35,000.

Answer 17

I got equation as 14000+3C...after that?

Answer 18

Solve for C, then A and B.

Answer 19

C=14000/3

Answer 20

No. 50,000=14,000+C

Answer 21

A=21000 B=17000 C=12000 now instead of 50000 I can put 35000 & solve for ABC?

Answer 22

A=16000 B=12000 C=7000 is it correct?

Answer 23

?

Answer 24

Not quite. You had A,B,C right. Consider the percentages.

Answer 25

plz help me

Answer 26

OK. A, B, and C are all out of 50,000. The percentage is just double the number of thousands (x,000/50,000 *100%=2x)

Answer 27

So A=42%, B=34%, and C=24%. Expressed as a ratio, that's \[0.42:0.34:0.24\] Multiply each of those by 35,000 and you have your answer.

Answer 28

got it
14700

Answer 29

I'm going to bed. I'll be back in the morning! Perhaps you should post separate questions on separate posts in future.

Answer 30

when u will be ol bcz I have some more quest...tell me whr to post the question bcz I can easily understand ur way of explaining.

Answer 31

You can always message me. I'll be back on some time in the next 24 hours, that's all I know at this point.

Answer 32

whr to msg u?
here only....or I can post u quest & u can give me ans

Answer 33

I am new to this site I dun know whr to msg?