(solved)Question 13 SSC-CGL 2020 March 3 Shift 1

Given x + y = 8, y + z = 13, z + x = 17, then the value of x²/yz = ?
(Rev. 05-May-2025)

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Question 13
SSC-CGL 2020 Mar 3 Shift 1

Given x + y = 8, y + z = 13, z + x = 17, then the value of x²/yz = ?

Solution in Short

Adding the three equations gives x + y + z = 19. Subtracting each of the given equations from this one, we get x = 6, y = 2 and z = 11. Finally, x²/yz = 18/11 ans!

Solution in Detail

Write the given equations like this:

x+y=8 . . . (1)\displaystyle x + y = 8\text{ . . . (1)}

y+z=13 . . . (2)\displaystyle y + z = 13\text{ . . . (2)}

z+x=17 . . . (3)\displaystyle z + x = 17\text{ . . . (3)}

Adding all the three equations,

2x+2y+2z=38\displaystyle 2x + 2y + 2z = 38

    x+y+z=19. . . (4)\displaystyle \implies x + y + z = 19 \text{. . . (4)}

Equation (4) - (1) gives z=11\displaystyle z = 11

Equation (4) - (2) gives x=6\displaystyle x = 6

Equation (4) - (3) gives y=2\displaystyle y = 2

x2yz=6×62×11=1811Ans\displaystyle \therefore \frac{x^2}{yz} = \frac{6 \times 6}{2 \times 11} = \frac {18}{11}\:\underline{Ans}

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