Question

if 40% of a mumber is equal to two-third of another number, what is the ratio of the first number to the second number?
1)7:3
2)2:5
3)3:7
4)5:3​

Answer 1

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• 40% of number is equal to ⅔ of another number.

${\bf{\blue{\underline{To\:Find:}}}}$

• The ratio of the first number to the second number.

${\bf{\blue{\underline{Now:}}}}$

• Let the first number be r.
• and second be m.

$\dagger \underline {\frak{ according \: to \: the \: ques : }}$

$: \implies{\bf{ 40\% r = \frac{2}{3} m}}$

$: \implies{\bf{ \frac{40r}{100} = \frac{2}{3} m}}$

$: \implies{\bf{ \frac{4r}{10} = \frac{2}{3} m}}$

$: \implies{\bf{ \frac{2r}{5} = \frac{2}{3} m}}$

$: \implies{\bf{ \frac{r}{m} = \frac{2}{3} \times \frac{5}{2} }}$

$: \implies{\bf{ \frac{r}{m} = \frac{ \cancel2}{3} \times \frac{5}{ \cancel2} }}$

$: \implies{\bf{ \frac{r}{m} = \frac{5}{ 3} }}$

$: \implies \boxed{\bf{ \purple{ r : m = 5 :3 } }}$

Hence option (4) is correct!!

Answer 2

Think outside the box. We know 100% of a number is itself.

We can observe 20% of the first number is 1/3 of the second number.

Now, what makes the first number 100%? It is the 5/3 of the second.

5/3 of the second number is equal to the first. So, the first number is 5/3 times the second one.

The portion is 5/3 : 1 = 5 : 3. So option 4 will be correct.