Question

If three times the larger of two numbers is divided by the smaller, the quotient and the remainder, each is equal to 6. If five times the smaller is divided by the larger, the quotient is 2 and the remainder is 3. The smaller number is:

Answer 1

let larger number be x

and smaller number be y

First condition

Dividend = divsor * quotient + remainder

3x= y*4+3

3x=4y+3

3x-4y=3

second condition

7y=5x+1

7y-5x=1

3 x -4 y = 3 .............1

-5 x + 7 y = 1 .............2

Eliminate y

multiply (1)by 7

Multiply (2) by 4

21 x -28 y = 21

-20 x + 28 y = 4

Add the two equations

1 x = 25

/ 1

x = 25

plug value of x in (1)

3 x -4 y = 3

75 -4 y = 3

-4 y = 3 -75

-4 y = -72

y = 18 1

x= 25

y= 18

Answer 2

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There is formula to find out dividend .

Dividend = quotient * divisor + remainder.

Now , assume there are two numbers ‘a’ and ‘b’. such that a > b ;

in the question it is given that 3 times of larger number when divided by smaller number then we get 6 as quotient and 6 as remainder.

divisor = b;

dividend = 3a;

quotient = 6;

remainder = 6;

using above formula we get the following equation.

3a = 6b + 6 ……….(1)

and one more equation according to question

divisor = a;

dividend = 5b;

quotient = 2;

remainder = 3;

5b = 2a + 3……..(2)

after solving equation 1 and 2 we get solution.

a= 16 ;

b = 7;

b is smaller then a , so anwer is b = 7;