Aptitude - Numbers - Discussion

Let the larger number is: X.

And the smaller number is: Y.

Now the relation one will be according to question.

(X-Y) = 1365....(i).

And other relation will be:

As we know that Dividend = Quotient*Divisor+Remainder;

We are given with Quotient = 6.

&& Remainder = 15.

Larger number = X = Dividend;

And Smaller number = Y = Divisor.

Now the equation will be:

Dividend = Quotient*Divisor+Remainder.

X = 6*Y+15.

X = 6Y+15.....(ii).

Now putting the value of X in equation (i) we get.

(X-Y) = 1365.

(6Y+15-Y) = 1365.

(5Y+15) = 1365.

5Y = 1350.

Y = 270 which is our Answer.

Let us assume the largest number is X & the Smallest number is Y.
The difference between two number is 1365.

So, X - Y=1365
X=1365+Y------------(1).

Now, assume the largest number is dividend, the smaller number is divisior
So, X is dividend & Y is divisior.
We know that,

Dividend= divisior*quostient + remainder.
X = Y * 6 + 15.
X = 6Y + 15------------> (2).

Let substitute eq(1) in eq(2).
1365 + Y = 6Y + 15.
Y - 6Y = 15 - 1365.
- 5Y = - 1350.

Here minus(-) minus(-) gets cancel.
So, 5Y = 1350.
Y= 1350/5.
Y=270.

Let the smaller number be= x.
Then the larger number be= x+1365.

We already have,
Quotient = 6,
Remainder= 15,
Divisor = x ( as in every division divisor is smaller than the dividend),
Dividend = x+1365.

As per formula,
Divisor = (dividend-remainder)/quotient.
=> x = (x+1365-15)/6,
=> x = (x+1350)/6,
=> 6x-x = 1350,
=> 5x = 1350,
=> x = 1350/5,
=> x = 270 (the smaller number) (answer).

Let the two numbers be x and y (x > y).

The difference between first and second number is 1365.

x - y = 1365...............(1).

When first number is divided by second 6 is the quotient and 15 is the remainder. This is written as:

x / y = 6 15/y (i.e. a mixed fraction).
x / y = (6y+15)/y (on simplifying the mixed fraction).

x = 6y + 15......................(2).

Solving (1) and (2), we get.

y = 270 ; x = 1635.

Difference of two numbers:
a- b = 1365.
a/b = 6 15/b.

a - b means 1 times of a is reduced from b and 15 extra part is remaining.
Also it is given that 6 times of b is leaving 15 as remainder;
So in a - b we only have 5 times b + 15.

Thus 1365-15/5 is the smallest number.
1365-15/5= 270.

For example
If a = 117 b = 17,
a-b = 100,
6b = 102,
5b = 85,
a/b leaves remainder 15.
So, a-b-15=85 which is equal to 5b.

It's simple.

lets take the larger number = (x) and smaller number = (y)
the difference between them is 1365
x-y = 1365 ---------- equation 1.
we know dividend = quotient * divisor + remainder
here the larger number is divided by smaller number
hence we get ,
6x + 15 = y
arranging it we get
6x - y = -15 ----------- equation 2.
adding both equation and solving them we get
y = 270.

Let us assume x as smaller number and y as the bigger one.

So, from the question,
y-x = 1365 --->1
y = 1365 + x --->2
From question,
y/x = 6 --->3
Gives, y = 6x. --->4

Sub 4 in 1,
6x - x = 1365
x = 273.

(Since leaves remainder 15 which is 5 ×3 =15. So, subtracting 3 from 273 to get the number that leaves no remainder)
So the number that leaves no remainder is 270.

@All.

Lets consider smaller number as X --->(i)
As per given difference of two numbers is 1365.

So consider larger number as X+1365 ---> (ii).

Dividend = quotient * divisor + remainder.
On dividing larger number by smaller number just put given values in above formula.
So we got equation as:
X+1365 = 6 * X + 15
5X = 1350.
X = 270 is smaller number.

Two numbers Difference is given I. e. 1365 one number =X(large) and another number(small)=Y.
X-Y=1365.

Large number divided by small number i.e
X/Y.....Y)X(6
/15

X=6Y+15 (above eqn. X-Y=1365then X=1365+Y).
1365+Y=6Y+15.
1365-15=6Y-Y i.e 1350=5Y.
Y=1350/5 i.e 270.

In problem asked smaller number that's why the ans is 270.

Lets say x is greater number and y is smallest number.
So first condition is x-y = 1365.

So second condition is y/x gives 6 as a quotient and 15 as a remainder.

According to formula (dividend)=(divisor*quotient)+remainder.
So x = 6y+15.

Putting x = 1365+y from first condition
y = 270.

Which is smaller number.