Home
Class 7
MATHS
If (1)/(x) : (1)/(y):(1)/(z) = 2 : 3 : 5...

If `(1)/(x) : (1)/(y):(1)/(z)` = `2 : 3 : 5`, then `x : y : z` = ?

A

`2 : 3 : 5`

B

`15 : 10 : 6`

C

`5 : 3 : 2`

D

`6 : 10 : 15`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we start with the given ratio: \[ \frac{1}{x} : \frac{1}{y} : \frac{1}{z} = 2 : 3 : 5 \] ### Step 1: Write the ratios in terms of fractions From the given ratio, we can express it as: \[ \frac{1}{x} = 2k, \quad \frac{1}{y} = 3k, \quad \frac{1}{z} = 5k \] where \( k \) is a constant. ### Step 2: Find expressions for \( x, y, z \) Now, we can find \( x, y, z \) by taking the reciprocal of each fraction: \[ x = \frac{1}{2k}, \quad y = \frac{1}{3k}, \quad z = \frac{1}{5k} \] ### Step 3: Find a common denominator To express \( x, y, z \) in the same ratio, we can find a common denominator. The least common multiple of the denominators \( 2k, 3k, 5k \) is \( 30k \). ### Step 4: Rewrite \( x, y, z \) in terms of the common denominator Now, we can express \( x, y, z \) using the common denominator: \[ x = \frac{15}{30k}, \quad y = \frac{10}{30k}, \quad z = \frac{6}{30k} \] ### Step 5: Form the ratio \( x : y : z \) Now we can write the ratio \( x : y : z \): \[ x : y : z = 15 : 10 : 6 \] ### Step 6: Simplify the ratio if necessary To simplify the ratio, we can divide each term by the greatest common divisor (GCD) of 15, 10, and 6, which is 1. Thus, the ratio remains: \[ x : y : z = 15 : 10 : 6 \] ### Final Answer Therefore, the final answer is: \[ x : y : z = 15 : 10 : 6 \] ---
Promotional Banner

Topper's Solved these Questions

  • RATION AND PROPORTION

    RS AGGARWAL|Exercise Test papers|18 Videos

  • RATION AND PROPORTION

    RS AGGARWAL|Exercise EXERCISE 8B|15 Videos

  • PROPERTIES OF TRIANGLES

    RS AGGARWAL|Exercise EXERCISE 15-D|18 Videos

  • RATIONAL NUMBERS

    RS AGGARWAL|Exercise TEST PAPER -(4)|17 Videos

Similar Questions

Explore conceptually related problems

If (1)/(x) : (1)/(y) : (1)/(z) = 2 : 3 : 5 then determine x : y :z

If (1)/(x):(1)/(y):(1)/(z)=2:3:5backslash then backslash x:y:z is equal to 2:3:5 b.15:10:6c.5:3:2d.6:10:15

If x + y + z = 12, x^(2) + Y^(2) + z^(2) = 96 and (1)/(x)+(1)/(x)+(1)/(z)= 36 . Then find the value x^(3) + y^(3)+z^(3).

If x+y+z=12 and x^(2)+y^(2)+z^(2)=96 and (1)/(x)+(1)/(y)+(1)/(z)=36 then the value x^(3)+y^(3)+z^(3) divisible by prime number is

If |(x^(n),x^(n+2),x^(n+3)),(y^(n),y^(n+2),y^(n+3)),(z^(n),z^(n+2),z^(n+3))| = (x -y) (y -z) (z -x) ((1)/(x) + (1)/(y) + (1)/(z)) , then n equals

x+y+z=15 if 9, x, y, z, a are in A.P. while (1)/(X)+(1)/(Y)+(1)/(Z)=(5)/(3)if9,X, Y, Z, a are in H.P., then the value of a will be -

Find the S.D. between the lines : (i) (x)/(2) = (y)/(-3) = (z)/(1) and (x -2)/(3) = (y - 1)/(-5) = (z + 4)/(2) (ii) (x -1)/(2) = (y - 2)/(3) = (z - 3)/(2) and (x + 1)/(3) = (y - 1)/(2) = (z - 1)/(5) (iii) (x + 1)/(7) = (y + 1)/(-6) = (z + 1)/(1) and (x -3)/(1) = (y -5)/(-2) = (z - 7)/(1) (iv) (x - 3)/(3) = (y - 8)/(-1) = (z-3)/(1) and (x + 3)/(-3) = (y +7)/(2) = (z -6)/(4) .

Show that the lines : (i) (x -5)/(7) = (y + 2)/(-5) = (z)/(1) " " and (x)/(1) = (y)/(2) = (z)/(3) (ii) (x - 3)/(2) = (y + 1)/(-3) = (z - 2)/(4) and (x + 2)/(2) = (y - 4)/(4) = (z + 5)/(2) are perpendicular to each other .

(2-3x)/(x)+(2-3y)/(y)+(2-3z)/(z)=0 then (1)/(x)+(1)/(y)+(1)/(z)=