# If two quantities x and y vary directly with each other, then

(a) x/y remains constant

(b) x - y remains constant

(c) x + y remains constant

(d) x × y remains constant

**Solution:**

If two quantities x and y vary directly with each other then x/y remains constant. This is the characteristic of direct proportion i.e. x/y = k which is the proportionality constant.

If two quantities x and y vary directly with each other, then x/y remains constant.

**✦ Try This: **If x and y are in direct proportion then the ratio of x/y or y/x is a constant, verify the following a) x/y remains constant b) x - y remains constant c) x + y remains constant d) xy remains constant

The following table depicts the direct proportion between two variables x and y

x |
18 |
45 |
90 |
225 |
150 |

y |
2 |
5 |
10 |
25 |
10 |

a) x/y = 18/2 = 45/5 = 90/10 = 225/25 = 150/10 = 15 = k = constant

b) x - y = 18 - 2 ≠ 45 - 5 ≠ 90 - 10 ≠ 225 - 25 ≠ 150 - 10 ≠ k ≠ constant

c) x + y = 18 + 2 ≠ 45 + 2 ≠ 90 + 10 ≠ 225 + 25 ≠ 150 + 10 ≠ k ≠ constant

d) xy = 18 × 2 ≠ 45 × 5 ≠ 90 × 10 ≠ 225 × 25 ≠ 150 × 10 ≠ k ≠ constant

Therefore if x and y are in direct proportion then only x/y remain constant. The remaining relations are incorrect i.e. x - y, x + y and xy are not constant.

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 13

**NCERT Exemplar Class 8 Maths Chapter 10 Problem 12**

## If two quantities x and y vary directly with each other, then (a) x/y remains constant, (b) x - y remains constant, (c) x + y remains constant, (d) x × y remains constant

**Summary:**

Food provisions for 100 people were there to last for 24 days. If 20 people left then 80 people will be left. The provisions will now last for 30 days

**☛ Related Questions:**

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