Ratio and Proportion Problems and Solutions for SSC and Bank Exams

Students face difficulties in ratio and proportion problems in competitive exams. If you don't want to face any difficulty related ratio and proportion problems, you should practice ratio and proportion problems with solutions for ssc and bank exams. 

Learn here in this blog, how to solve ratio and proportion problems with examples and different-2 equations. It is a good idea if you are doing a practice of ratio and proportion questions and answers because these are the important questions which asked mostly in competitive exams.

Ratio and Proportion Problems and Solutions for Competitive Exams

Q.1. If a : b = 5 : 9 and b : c = 4 : 7, find a : b : c.

Solution: 

$$a : b = 5 : 9 \ and \ b : c = 4 : 7 =\left(4×{9\over4}\right):\left(7×{9\over4}\right)=9:{63\over4}  $$

  $$→ a : b:c=5:9:{63\over4}=20:36:63.$$

Q.2. Divide Rs. 672 in the ratio 5 : 3.

Solution:

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

$$∴ First \ part= Rs.\left(672×{5\over8} \right)= Rs. 420;$$

  $$∴ Second \ part= Rs.\left(672×{3\over8} \right)= Rs. 252;$$

Q.3. Divide Rs. 1162 among A, B, C in the ratio 35 : 28 : 20.

Solution: 

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

$$∴ A's \ Share= Rs.\left(1162×{35\over83} \right)= Rs. 490;$$

  $$B's \ Share = Rs.\left(1162×{28\over83} \right)=Rs.392;$$

  $$C's \ Share = Rs.\left(1162×{20\over83} \right)=Rs.280. $$

Q.4. A bag contains 50p, 25p and 10p coins be 5x, 9x and 4x respectively.

Solution: 

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

$$Then,{5x\over2}+{9x\over4}+{4x\over10}=206$$

↔ 50x + 45x + 8x = 4120 ↔ 103x = 4120 ↔ x = 40.

∴ Number of 50 p coins = (5×40)=200; Number of 25 p coins = (9×40)= 360;

Number of 10 p coins = (4×40)=160

Q.5. 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.

Solution: 

Let the quantity of alcohol and water be 4x litres and 3x litres respectively. Then,

$$ {4x\over3x+5}= {4\over5}↔20x=4(3x+5)↔8x=20↔x=25. $$

∴ Quantitative of alcohol = (4×2.5)/ litres = 10 / letres

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