**This is Part 01 of Quantitative Aptitude chapter Ratio and Proportion. If you are preparing for any government exam like CAT, GMAT, SSC, Banking etc, make sure you practice each of the questions given. **

**(01)** **If a:b = 7:9 and b:c = 5:7, then what is a:c**

Sol:

LCM of 9 and 5 is 45

Then, a:b:c = 35: 45: 63, thus a:c = 35:63, a:c = 5:9

**Ans: 5:9**

**02. The ratio of two numbers is 3:8 and their difference is 115. The smaller of the two numbers is:**

Sol:

First number = 3x, Second number = 8x

8x – 3x = 115, 5x = 115, x = 23

Smaller number = 3x = 3 (23) = 69

**Ans is 69**

**03. Four numbers are in the ratio 1:2:3:4. Their sum is 16. The sum of the first and fourth number is equal to:**

Sol:

First number = x,

Second number = 2x,

Third number = 3x,

Fourth number = 4x

Sum of all the number is 16

Hence,

x + 2x + 3x + 4x = 16

10x = 16

x = 16/10 = 8/5,

First number = 8/5 and Fourth number = 4(8/5) = 32/5

Thus, required sum = 8/5 + 32/5 = 40/5 = 8**The answer is 8**

**04. A and B have money in the ratio 2:1. If A gives Rs. 2 to B, the money will be in the ratio 1:1. What were the initial amounts they had?**

Sol:

A = 2x,

B = x

A gives Rs. 2 to B

So Money left with A = 2x-2

And Money left with B = x+2

**New ratio is 1:1**

2x – 2 / x + 2 = 1 / 1

2x – 2 = x + 2

x = 4,

Thus, **A = Rs. 8** and **B = Rs. 4**

**05. By mistake instead of dividing Rs. 117 among A, B and C in the ratio ½ : 1/3 : ¼, it was divided in the ratio of 2:3:4. Who gains the most and by how much?**

Sol:

A’s initial share = 2/9 × 117 = Rs. 26

B’s initial share = 3/9 × 117 = Rs. 39

C’s initial share = 4/9 × 117 = Rs. 52

A’s original share = ½ : 13/12 × 117 = ½ × 12/13 × 117 = Rs. 54

B’s original share = 1/3 : 13/12 × 117 = 1/3 × 12/13 × 117 = Rs. 36

C’s original share = ¼ : 13/12 × 117 = ¼ × 12/13 × 117 = Rs. 27

**A gains the most and by Rs. ( 54 – 26) = Rs. 28**

**06. Divide Rs. 1250 among A, B and C so that A gets 2/9 of B’s share, and C gets ¾ of A’s share.**

Sol:

B’s share = x,

A’s share = 2x/9 and

C’s share = ¾ of (2x/9) = x/6

x + 2x/9 + x/6 = 1250

25x/18 = 1250

x = Rs. 900

**B’s share = Rs. 900**, **A’s share = 200** and **C’s share = Rs. 150**

**07. If x:y = 3:1, then x³ – y³ : x³ + y³ = ?**

Sol: x/y = 3/1, therefore, x = 3y

Thus, x³ – y³ / x³ + y³ => ** 27y³ – y³** / **27y³ + y³** = 26y³ / 28y³ = 13:14

**Hence 13:14 is the answer**

**08. The fourth proportional to 12, 21, 8 is:**

Sol: 12/21 = 8/x

12 × x = 21 × 8

x = 14

**Answer is 14**

**09. The ratio of 2 ^{1.5 }: 2^{0.5 }is:**

Sol: 2^{1.5 }: 2^{0.5}

= 2^{1.5-0.5 }= 2^{1 }= 2 = 2:1

**Hence 2:1 is the right answer**

**10. If m:n = 3:2, then (4m + 5n) : (4m – 5n) is equal to:**

Sol: m:n = 3:2, thus, 4m: 5n = 12 : 10,

**Hence 11: 1 is the right answer**