Question

1. Two numbers are in the ratio 7:4 and their difference is 144. Find the numbers.​

Answer 1

$\huge\mathbb{SOLUTION}$

• Let the number be n

• So 7n and 4n

• Their difference=144

Now

$\bf\underline{\red{\:\:\:\:\:\:\:\:A.T.Q:-\:\:\:\:\:\:\:}}$

$\sf\implies 7n-4n=144\\ \\ \sf\implies 3n=144\\ \\ \sf\implies n=\cancel{\dfrac{144}{3}}\\ \\ \sf\implies n=48$

So the value of n is 48

Now the numbers

$\sf\bullet 7n= 7\times 48\\ \sf\implies 336\\ \\ \sf\bullet 4n =4\times 48\\ \sf\implies 192$

$\boxed{\sf{The\: number's\:are\:336\:\:and\:\:192}}$

Answer 2

Solution

Given

• The required numbers are in the ratio 7 : 4

• Difference of the numbers is 144

Let x be the common multiple of both the numbers

• The numbers would be of the form 7x and 4x

According to the Question,

$\sf \: 7x \: - 4x = 144 \\ \\ \implies \: \sf \: 3x = 144 \\ \\ \implies \: \boxed{ \boxed{ \sf{x = 48}}}$

Now,

The numbers would be :

• 7x = 7 × 48 = 336

• 4x = 4 × 48 = 192

The required numbers are 336 and 192