Math, asked by kumarraghav85, 1 year ago

The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is:

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Answers

Answered by rajsingh24
71

\large{\underline{\underline{\mathfrak\green{Question\::}}}}

The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is.

\large{\underline{\underline{\mathfrak\red{SOLUTION\::}}}}

\implies let the three numbers be p, q & r .

\implies sum of the numbers is 98.

\implies p+ q + r= 98 -------(1)

\implies the ratio of the first to the second is 2/3.

\rightarrow p/q= 2/3.

\rightarrow p = 2/3 × q.

\rightarrow \orange{\boxed{p= 2q/3.}}

\implies the ratio of the second to the third is 5/8.

\rightarrow q/r= 5/8

\rightarrow r/q= 8/5

\rightarrow r = 8/5 × q

\rightarrow \green{\boxed{r= 8q/5}}

\implies put the value of p= 2q/3 & r= 8q/5 in equ. (1)

\rightarrow 2q/3 + q+ 8q/5=98

\rightarrow 49q/15 = 98

\rightarrow 49 q = 98 ×15

\rightarrow 49 q= 1470

\implies \red{\boxed{q = 30}}

.°. the second the number is 30.

Answered by Anonymous
44

Given :

  • The sum of three numbers is 98.
  • The ratio of the first to the second is 2/3.
  • The ratio of the second to the third is 5/8.

To find :

  • The second number

Solution :

Let the first number be x.

Let the second number be y.

Let the third number be z.

As per first condition :

  • The sum of three numbers is 98.

x + y + z = 98 ----> (i)

As per second condition :

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

\mathtt{\dfrac{x}{y}} = \mathtt{\dfrac{2}{3}}

\mathtt{3x\:=\:2y}

\mathtt{\dfrac{x}{y}=\:{\dfrac{2y}{3}}} ----> (ii)

As per the third condition :

  • The ratio of the second to the third is 5/8.

\mathtt{\dfrac{y}{z}} = \mathtt{\dfrac{5}{8}}

\mathtt{8y\:=\:5z}

\mathtt{\dfrac{8y}{5}\:=\:z} ----> (iii)

Substite values of eqn. 2 and eqn. 3 in eqn. 1,

\mathtt{\dfrac{2y}{3}} + \mathtt{y} + \mathtt{\dfrac{8y}{5}\:=\:z} = \mathtt{98}

\mathtt{\dfrac{2y\:+\:3y}{3}\:+\:{\dfrac{8y}{5}}} = \mathtt{98}

\mathtt{\dfrac{5(2y+3y)\:+\:8(3y)}{15}} = \mathtt{98}

\mathtt{\dfrac{10y\:+\:15y\:+\:24y}{15}} = \mathtt{98}

\mathtt{\dfrac{25y\:+\:24y}{15}} = \mathtt{98}

\mathtt{49y\:=\:98\:\times\:15}

\mathtt{49y\:=\:1470}

\mathtt{y\:=\:{\dfrac{1470}{49}}}

\mathtt{y\:=\:30}

\bold{\large{\boxed{\rm{\red{Second\:Number\:=\:y\:=30}}}}}

First Number :

\mathtt{x\:=\:{\dfrac{2y}{3}}}

\mathtt{x\:=\:{\dfrac{2\:\times\:30}{3}}}

\mathtt{x\:=\:{\dfrac{60}{3}}}

\mathtt{x\:=\:20}

\bold{\large{\boxed{\rm{\blue{First\:Number\:=\:x\:=20}}}}}

Third Number :

\mathtt{z\:=\:{\dfrac{8y}{5}}}

\mathtt{z\:=\:{\dfrac{8\:\times\:30}{5}}}

\mathtt{z\:=\:{\dfrac{240}{5}}}

\mathtt{z=48}

\bold{\large{\boxed{\rm{\pink{Third\:Number\:=\:z\:=48}}}}}

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