Question

Two numbers are in the ratio 2:3. If 8 is subtracted from both, the new numbers have a ratio of 6:11. Find the bigger number. *

25

30

20

35

​

Answer 1

Working out:

It is given in the question that two numbers are in the ratio 2 : 3. So, let the numbers be 2x and 3x because they are in ratio, x can cancel out later.

Now, 8 is subtracted from both numbers. It means:

• First number = 2x - 8
• Second number = 3x - 8

And, now these new numbers are in the ratio 6:11, so we can represent this data in the form:

$\sf{ \longrightarrow{ \dfrac{2x - 8}{3x - 8} = \dfrac{6}{11} }}$

Now, cross multiplying,

$\sf{ \longrightarrow{11(2x - 8) = 6(3x - 8)}}$

Opening the parentheses,

$\sf{ \longrightarrow{22x - 88 = 18x - 48}}$

Here we want to find the value of x, So we will isolate x in any one side of the equation.

$\sf{ \longrightarrow{22x - 18x = - 48 + 88}}$

Solving further,

$\sf{ \longrightarrow{4x = 40}}$

$\sf{ \longrightarrow{x = \dfrac{40}{4} }}$

$\sf{ \longrightarrow{x = \boxed{10}}}$

Now finding the original numbers,

• First number = 2x = 20
• Second number = 3x = 30

So, the bigger number is 30 (Option B)

Quick check:

When 8 is subtracted from 20 and 30, we get 12 and 22 respectively, and 12/22 = 6/11 which is our second ratio.

Hence, verified !!

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Answer 2

Step-by-step explanation:

GIVEN:

TWO NUMBERS ARE IN THE RATIO 2:3 AND 8 IS SUBTRACTED FROM BOTH AND OBTAIN A NEW RATIO OF 6:11.

TO FIND:

THE BIGGER NUMBER AMONG 2.

SOLUTION:

LET THE TWO NUMBERS BE 2X AND 3X.

8 IS SUBTRACTED FROM BOTH THE NUMBERS:

2X-8

3X-8

ATQ,

$\frac{2x - 8}{3x - 8} = \frac{6}{11} \\ \\ = > 11(2x - 8) = 6(3x - 8) \\ \\ = > 22x - 88 = 18x - 48 \\ \\ = > 22x - 18x = - 48 + 88 \\ \\ = > 4x = 40 \\ \\ = > x = \frac{40}{4} = 10$

WE GOT X=10

NOW THE BIGGER NUMBER = 3X= 3×10=30.

SMALLER NUMBER =2X=2×10=20.

HENCE THE BIGGER NUMBER IS 30.