Question

the number are in the ratio 7:11 if 7 is added to each other of the number the ratio become 2:3 find the number ​

Answer 1

$\sf{\star}$ Correct Question:-

Two numbers are in the ratio 7:11. If 7 is added to both the numbers the ratio becomes 2:3. Find the numbers.

$\sf{\star}$ Given:-

• Two numbers are in the ratio = 7:11
• When 7 is added to both the ratio becomes = 2:3

$\sf{\star}$ To Find:-

The numbers.

$\sf{\star}$ Assumption:-

Let the common multiples of the ratios be x

Therefore,

1st number = 7x

2nd number = 11x

$\sf{\star}$ Solution:-

When 7 is added to both the number the ratio becomes 2:3

ATQ,

$\sf{\dfrac{7x+7}{11x+7} = \dfrac{2}{3}}$

= $\sf{3(7x+7) = 2(11x+7)}$

= $\sf{21x + 21 = 22x + 14}$

= $\sf{21x - 22x = 14 - 21}$

= $\sf{-x = -7}$

= $\sf{x = 7}$

Therefore,

The numbers are:-

1st number = 7x = 7×7 = 49

2nd number = 11x = 11×7 = 77

______________________________________

$\sf{\star}$ Verification:-

The ratio of the two numbers should be 7:11

Therefore,

$\sf{49:77}$

= $\sf{\dfrac{49}{77}}$

Cancel both numerator and denominator by 7

= $\sf{\dfrac{\cancel{49}}{\cancel{77}}}$

= $\sf{\dfrac{7}{11}}$

= $\sf{7:11}$

Therefore the ratio of the numbers is 7:11 [Verified].

______________________________________

Answer 2

Here, as per the provided question we are said here to find the number, where there is given information....

But, in the question we can see that there's a bit mistake. So, first of all let us correct the question and then write the answer –

★ CORRECT QUESTION :

Two numbers are in the ratio 7:11. If 7 is added to each other of the numbers then the ratio becomes 2:3. Find the numbers.

GIVEN :

• Two numbers are in the ratio as = 7:11

• When a number (considered as 7) is is added to each each other of the number then, the ratio becomes as = 2:3

TO FIND :

• The number = ?

(when the provided question is given there with an appropriate information).

STEP-BY-STEP EXPLAINATION :

Now, there is given two numbers in the ratio as 7 and 11, When they're considered after putting as x, then we'll write them respectively as –

⟼ First number (7) = 7 × x = 7x

⟼ Second number (11) = 11 × x = 11x

Hence, we will simplify now as per the provided question (with taking as 'x')

$⟹ \: \frac{7 \rm {x} \: + \: 7 }{11 \rm {x} \: + \: 7} = \: \frac{2}{3}$

Now, solving here in the type of equation

'L.H.S = R.H.S' Rule –

$⟹ \: 3(7 \rm {x} \: + \: 7) \: = 2(11 \rm {x} \: + \: 7)$

$⟹ \: 21 \rm {x} \: + \: 21 \: = \: 22 \rm {x} \: + \: 14$

$⟹ \: 21 \rm {x} \: - \: 22 \rm {x} \: = \: 14 \: - \: 21$

$⟹ \rm { - x} \: = \: - 7$

$⟹ \rm {x} \: = \: 7$

Hence,

We have got here the numbers as (after solving this question in the form of equation) –

⟼ First number = (7) = 7 × 7 = 49

⟼ Second number = (11) = 11 × 7 = 77

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