Question

11.)
n-m
12. Two numbers are in ratio 4 : 7. If 3 is added to each number, the ratio becomes 5 : 8. Find the
numbers.
which is the greater: 3:4 or 2:37​

Answer 1

Appropriate Question :-

(1) Two numbers are in ratio 4 : 7. If 3 is added to each number, the ratio becomes 5 : 8. Find the numbers.

(2) Which is the greater: 3:4 or 2:37?

Explanation :-

$\green\bigstar$ (1)

Given :

• Two numbers are in ratio 4 : 7.

• The ratio becomes 5 : 8 when 3 is added to each of them.

To Find :

• The Numbers.

Solution :

Let the Numbers be 4x and 7x.

According to the Question,

$\sf\implies{ \dfrac{4x + 3}{7x + 3} = \dfrac{5}{8} }$

$\sf\implies{8(4x + 3) = 5(7x + 3)}$

$\sf\implies{32x + 24 = 35x+ 15}$

$\sf\implies{32x - 35x= 15 - 24}$

$\sf\implies{ - 3x = - 9}$

$\sf\implies{3x = 9}$

$\sf\implies{x = \dfrac{9}{3} }$

$\implies\boxed{\textsf{\textbf\red{x = 3}}}$

Therefore, The numbers are :-

• 4x = 12.
• 7x = 21.

$\green\bigstar$ (2)

We have to find which is the greater:-

3:4 or 2:37.

Put them equal.

$\sf\implies{ \dfrac{3}{4} = \dfrac{2}{37} }$

Cross Multiply them.

$\sf\implies{3(37) = 2(4)}$

$\sf\implies{111 = 8}$

As, we can clearly see that, 111 is greater than 8.

So, 3 : 4 is greater.

Answer 2

1. The numbers are 12 and 21
2. 3 : 4 is greater.

Step by step explanation :-

$\huge{\green{\sf{⇝1)}}}$

Question :-

Two numbers are in ratio 4 : 7. If 3 is added to each number, the ratio becomes 5 : 8. Find the numbers.

Solution :-

Let the numbers in the ratio 4 : 7 be 4x and 7x respectively.

$\sf{Given:-}$

• ★ If three is added to each number the ratio will be 5 : 8

The equation derived :-

$\green{\boxed{\sf{\dfrac{4x+3}{7x+3}=\dfrac{5}{8}}}}$

• Using cross multiplication

$\green{\leadsto{\sf{8(4x+3)=5(7x+3)}}}$

$\green{\leadsto{\sf{(32x+24=35x+15)}}}$

$\green{\leadsto{\sf{(35x-32x=24-15)}}}$

$\green{\leadsto{\sf{(3x=9)}}}$

$\green{\leadsto{\sf{(x=\cancel\dfrac{9}{3})}}}$

$\green{\leadsto{\sf{x=3}}}$

We get,

x = 3

Therefore the numbers are :-

➝4x= 4(3) = 12

➝7x= 7(3) = 21

$\huge{\green{\sf{⇝2)}}}$

Question :-

Which is the greater: 3 : 4 or 2 : 37 ?

Solution :-

3 : 4 can also be written as $\sf{\frac{3}{4}}$

And,

2 : 37 can be written as $\sf{\frac{2}{37}}$

➝The L.C.M of 4 and 37 is 148

Therefore,

$\sf{\frac{3}{4}=\frac{444}{148}(Using~the~L.C.M)}$

And,

$\sf{\frac{2}{37}=\frac{296}{148}(Using~the~L.C.M)}$

Clearly:-

$\sf{\frac{444}{148}~is~greater~than\:\frac{296}{148}}$

Therefore the ratio 3 : 4 is greater .