# The three numbers are in the ratio 4:5:6. If the sum of the largest and the smallest number is equal to the sum of the secon

The three numbers are in the ratio 4:5:6. If the sum of the largest and
the smallest number is equal to the sum of the second largest number
and 55. Find the numbers.

### Given :-

• The three numbers are in the ratio of 4 : 5 : 6.
• The sum of the largest and the smallest number is equal to the sum of the second largest number and 55.

### To Find :-

• What are the numbers.

### Solution :-

Let,

$$\mapsto$$ First number = 4x

$$\mapsto$$ Second number = 5x

$$\mapsto$$ Third number = 6x

According to the question,

$$\implies \sf 6x + 4x =\: 5x + 55$$

$$\implies \sf 10x =\: 5x + 55$$

$$\implies \sf 10x – 5x =\: 55$$

$$\implies \sf 5x =\: 55$$

$$\implies \sf x =\: \dfrac{\cancel{55}}{\cancel{5}}$$

$$\implies \sf x =\: \dfrac{11}{1}$$

$$\implies \sf\bold{\green{x =\: 11}}$$

Hence, the required numbers are :

$$\dashrightarrow$$ First number :

$$\leadsto \sf 4x$$

$$\leadsto \sf 4(11)$$

$$\leadsto \sf 4 \times 11$$

$$\leadsto \sf\bold{\red{44}}$$

$$\dashrightarrow$$ Second number :

$$\leadsto \sf 5x$$

$$\leadsto \sf 5(11)$$

$$\leadsto\sf 5 \times 11$$

$$\leadsto \sf\bold{\red{55}}$$

$$\dashrightarrow$$ Third number :

$$\leadsto \sf 6x$$

$$\leadsto \sf 6(11)$$

$$\leadsto \sf 6 \times 11$$

$$\leadsto \sf\bold{\red{66}}$$

$$\therefore$$ The numbers are 44 , 55 and 66 respectively.

$$\rule{150}{2}$$

### VERIFICATION :-

$$\Rightarrow \sf 6x + 4x =\: 5x + 55$$

By putting x = 11 we get,

$$\Rightarrow \sf 6(11) + 4(11) =\: 5(11) + 55$$

$$\Rightarrow \sf 66 + 44 =\: 55 + 55$$

$$\Rightarrow \sf\bold{\purple{110 =\: 110}}$$

Hence, Verified.

$$\rule{150}{2}$$

3 Sum of three numbers which are in the ratio 3:4:5 is 60. What is the sum of their squares?

(A)1970

(B)1430

(C)1250

(D)1760

https://brainly.in/question/40125762

2. Provided: The three numbers are in the ratio 4:5:6. & sum of the largest and smallest number is equal to the sum of 2nd largest no. and 55.

Need to find: The three respective numbers.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

❍ Let’s say, that the three numbers which are in the ratio be 4x, 5x and 6x.

⠀⠀⠀⠀

$$\underline{\bigstar\:\pmb{ \frak{According \: to \: the \: given \: Question :}}}$$

• Given condition, if sum of the largest and smallest number is equal to the sum of 2nd largest no. and 55.

$$:\implies\sf Largest \: no. + Smallest \: no. = 2nd \: largest \: no. + 55 \\\\\\:\implies\sf 6x + 4x = 5x + 55 \\\\\\:\implies\sf 10x = 5x + 55 \\\\\\:\implies\sf 10x – 5x = 55\\\\\\:\implies\sf 5x = 55\\\\\\:\implies\sf x = \cancel\dfrac{55}{5}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 11}}}}}\;\bigstar$$

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Therefore,

⠀⠀⠀⠀

• First no. 4x, 4(11) = 44
• Second no. 5x, 5(11) = 55
• Third no. 6x = 6(11) = 66

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$$\therefore{\underline{\textsf{Hence, the three numbers are \textbf{44, 55 \sf{and} \textbf{66} \sf{respectively}.}}}}$$⠀⠀⠀⠀