Two numbers are in the ratio 5:4 and their sum is 54 then find those numbers

We will follow the rules of dividing a quantity in a given ratio (two or three) to solve different types of problems.

1. 20 apples are distributed between Aaron and Ben in the ratio 2 : 3. Find, how many does each get?

Solution:

Aaron and Ben get apples in the ratio 2 : 3 i.e. if Aaron gets 2 parts, B should get 3 parts.

In other words, if we make (2 + 3) = 5 equal parts, then Aaron should get 2 parts out of these 5 equal part

i.e. Aaron gets = 2/5 of the total number of apples = 2/5 of 20 = 2/5 × 20 = 8 apples

Similarly, Ben gets 3 parts out of 5 equal parts

i.e. Ben gets = 3/5 of the total number of apples = 3/5 of 20 = 3/5 × 20 = 12 apples

Therefore, Aaron gets 8 apples and Ben gets 12 apples.

In other way we can solve this by the direct method,

Since, the given ratio = 2 : 3 and 2 + 3 = 5

Therefore, Aaron gets = 2/5 of the total number of apples

= 2/5 × 20 apples = 8 apples

and, Ben gets = 3/5 of the total number of apples

= 3/5 × 20 apples = 12 apples

2. Divide $ 120 between David and Jack in the ratio 3 : 5.

Solution:

Ratio of David’s share to Jack’s share = 3 : 5

Sum of the ratio terms = 3 + 5 = 8

Thus we can say David gets 3 parts and Jack gets 5 parts out of every 8 parts.

Therefore, David’s share = $(3 × 120)/8 = $45

And, Jack’s share = $(5 × 120)/8 = $75

Therefore, David get $45 and Jack gets $75

More solved problems on dividing a quantity in a given ratio:

3. Divide $260 among A, B and C in the ratio 1/2 : 1/3 : 1/4.

Solution:

First of all convert the given ratio into its simple form.

Since, L.C.M. of denominators 2, 3 and 4 is 12.

Therefore, 1/2 : 1/3 : 1/4 = 1/2 × 12 : 1/3 × 12 : 1/4 × 12 = 6 : 4 : 3

And, 6 + 4 + 3 = 13

Therefore, A’ share = 6/13 of $260 = $6/13 × 260 = $120

B’ share = 4/13 of $260 = $4/13 × 260 = $80

C’ share = 3/13 of $260 = $3/13 × 260 = $60

Therefore, A get $120, B gets $80 and C gets $60

4. Two numbers are in the ratio 10 : 13. If the difference between the numbers is 48, find the numbers.

Solution:

Let the two numbers be 10 and 13

Therefore, the difference between these numbers = 13 – 10 = 3

Now applying unitary method we get,

When difference between the numbers = 3; 1st number = 10

⇒ when difference between the numbers = 1; 1st number = 10/3

⇒ when difference between the numbers = 48; 1st number = 10/3 × 48 = 160

Similarly, in the same way we get;

When difference between the numbers = 3; 1st number = 13

⇒ when difference between the numbers = 1; 1st number = 13/3

⇒ when difference between the numbers = 48; 1st number = 13/3 × 48 = 208

Therefore, the required numbers are 160 and 208.

The above examples on dividing a quantity in a given ratio will give us the idea to solve different types of problems on ratios.

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Question 10 Exercise 12(D)

Answer:

Solution:

Let the first even number = x

second even number = x + 2

and third even number = x + 4

According to the condition,

$x+x+2+x+4=54$

$\Rightarrow3x+6=54$

$\Rightarrow3x=54-6$

$⇒x=\frac{48}{3}$

$\Rightarrowx=16$

∴ First even number =x= 16

Second even number = x+2 = 16 + 2 = 18

and third even number = x+3 = 16 + 4 = 20

Hence, the three consecutive even numbers are 16, 18 and 20.

Video transcript

Hello students, welcome to little homework. My name is virtual. And today we are going to solve the following question. The sum of two numbers is 18 if one is twice the other finder number. So so here. Going to other finder numbers. Nothing is mentioned, unfortunately. Thank you for watching

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