**Direction To Solve**

**Choose the correct option in questions related to Ration and Proportion**
**1-** If a : b = 5 : 9 and b : c = 4: 7, find a : b : c?

Answer & Explanation

Answer - **A** (20:36:63)

Explanation - a:b=5:9 and b:c=4:7

= (4x9/4): (7x9/4) = 9:63/4

a:b:c = 5:9:63/4 =20:36:63

**2-** Find the fourth proportional to 4, 9, 12?

Answer & Explanation

Answer - **C** (27)

Explanation - Let the fourth proportional to 4, 9, 12 be a.

Then, 4 : 9 : : 12 : a

4 a =9 x 12

a=(9 x 12)/14=27;

Fourth proportional to 4, 9, 12 is 27

**3-** If x : y = 3 : 4, find (4x + 5y) : (5x - 2y)?

Answer & Explanation

Answer - **B** (32/7)

Explanation - x/y=3/4

(4x+5y)/(5x+2y)= (4( x/y)+5)/(5 (x/y)-2)

=(4(3/4)+5)/(5(3/4)-2)

=(3+5)/(7/4)=32/7

**4-** Divide Rs. 672 in the ratio 5 : 3?

Answer & Explanation

Answer - **A** (420 and 252)

Explanation - Sum of ratio terms = (5 + 3) = 8.

First part = Rs. (672 x (5/8)) = Rs. 420;

Second part = Rs. (672 x (3/8)) = Rs. 252

**5-** Divide Rs. 1162 among A, B, C in the ratio 35 : 28 : 20?

Answer & Explanation

Answer - **C** (490 , 392 and 280)

Explanation - Sum of ratio terms = (35 + 28 + 20) = 83.

A's share = Rs. (1162 x (35/83))= Rs. 490;

B's share = Rs. (1162 x(28/83))= Rs. 392;

C's share = Rs. (1162 x (20/83))= Rs. 280

**6-** A bag contains 50 p, 25 p and 10 p coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of 25 paisa type?

Answer & Explanation

Answer - **B** (360)

Explanation - Let the number of 50 p, 25 P and 10 p coins be 5x, 9x and 4x respectively.

(5x/2)+( 9x/ 4)+(4x/10)=206

50x + 45x + 8x = 4120

103 x = 4120

x=40.

Number of 50 p coins = (5 x 40) = 200;

Number of 25 p coins = (9 x 40) = 360;

Number of 10 p coins = (4 x 40) = 160.

**7-** A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture?

Answer & Explanation

Answer - **A** (10)

Explanation - Let the quantity of alcohol and water be 4x litres and 3x litres respectively

4x/(3x+5)=4/5

20x=4(3x+5)

8x=20

x=2.5

Quantity of alcohol = (4 x 2.5) litres = 10 litres