Question

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.

Answer 1

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.

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

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

• 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,

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

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

Answer 2

Answer:

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.

$\rule{150}{2}$

#Learn more :

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

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