Question

The sum of three numbers is 350. If the ratio of the first to the second is 23, and that of the second to
the third is 45, then what is the second number?​

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

GiveN:

• Sum of 3 numbers = 350
• Ratio of 1st to 2nd = 2:3
• Ratio of 2nd to 3rd = 4:5

To FinD:

• Second number?

Step-by-Step Explanation:

Let the numbers be A, B and C

According to question,

1. A:B = 2:3
2. B:C = 4:5

Both the ratio have B in common, hence we need to express the three numbers into one ratio.

Here,

• LCM of 3 and 4 is 12

×plying 4 with (1) and ×plying 3 with (2),

1. A:B = 8:12
2. B:C = 12:15

Then, A:B:C = 8:12:15

Let the numbers be 8x, 12x and 15x.

According to question,

⇒ Sum of all three numbers = 350

⇒ 8x + 12x + 15x = 350

⇒ 35x = 350

⇒ x = 10

Then,

The second number is:

$\huge{ \boxed{ \sf{ \red{12(10) = 120}}}}$

Answer 2

Given :

• The sum of three numbers is 350.

• if the ratio of the first to the second is 2/3,

• the second to the third is 4/5,

To Find :

• what is the second number?

Solution :

Let the three numbers be x, y and z.

Sum of the numbers is 350

x + y + z = 350 ………………( 1 )

The ratio of the first to the second is 2/3

x/y = 2/3

x = 2y/3

The ratio of the second to the third is 4 /5

y/z = 4/5

z = 5y/4

Put the value of x = 2y/3 and z = 5y/4 in (i).

2y/3 + y + 5y /4 = 350

8y + 12y + 15y / 12 = 350

35y = 350 × 12

y = 350 × 12 / 35

y = 120

• Therefore, the second number is 120.