Ratio and Proportion problems
- 1. In a zoo, there are rabbits and pigeons. If heads are counted, there are 340 heads and if legs are counted there are 1060 legs.How many pigeons are there?
Options- A. 120
- B. 150
- C. 170
- D. 180 Discuss
Correct Answer: 150
Explanation:
Suppose there are all the pigeons then total no of heads are 340 and total no of legs are 680.
Now, since 380 (1060-680) legs are extra, it means there will be 190 (380/2) rabbits.As we know a rabbit has two extra legs than that of a pigeon.
Therefore, number of rabbits =190
and number of pigeons = 340- 190 = 150
- 2. Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats ?
Options- A. 1:2:3
- B. 2:3:4
- C. 3:4:5
- D. 4:5:6 Discuss
Correct Answer: 2:3:4
Explanation:
Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
? [(140/100) × 5x],[(150/100) × 7x] and [(175/100) × 8x]
? 7x, 21x/2 and 14x.
? The required ratio =7x : 21x/2 : 14x
? 14x : 21x : 28x
? 2 : 3 : 4
- 3. The third proportional to 9 and 12 is ?
Options- A. 14
- B. 16
- C. 18
- D. 20 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 16
Explanation:
Let the third proportion to 9 & 12 be 'x'.
=> 9:12 = 12 :p
=> p = 12x12/9 = 16.
- 4. The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Rs. 6000. By what percent is the salary of C more than that of A?
Options- A. 100 %
- B. 200%
- C. 300%
- D. 600% Discuss
Correct Answer: 200%
Explanation:
Let the salaries of A, B, C be x, 2x and 3x respectively.
Then,2x + 3x = 6000 => x = 1200.
A's salary = Rs. 1200, B's salary = Rs. 2400, and Cs salary Rs. 3600.
Excess of C's salary over A's=[ (2400 /1200) x 100] = 200%.
- 5. A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
Options- A. 9:5
- B. 2:3
- C. 4:7
- D. 5:6 Discuss
Correct Answer: 9:5
Explanation:
Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5.
- 6. In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
Options- A. 100
- B. 250
- C. 260
- D. 416 Discuss
Correct Answer: 416
Explanation:
Let the number of boys and girls be 8x and 5x.
Total number of students = 13x = 13 * 32 = 416.
- 7. The concentration of petrol in three different mixtures (petrol and kerosene) is 1/2 , 3/5 and 4/5 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. what is the ratio of petrol and kerosene in the new mixture?
Options- A. 4:5
- B. 3:2
- C. 3:5
- D. 2:3 Discuss
Correct Answer: 3:2
Explanation:
Concentration of petrol in A B C
1/2 3/5 4/5
Quantity of petrol taken from A = 1 litre out of 2 litre
Quantity of petrol taken from B = 1.8litre out of 3 litre
Quantity of petrol taken from C = 0.8 litre out of 1 litre
Therefore, total petrol taken out from A, B and C = 1+1.8+0.8 =3.6 litres
So, the quantity of kerosen =(2+3+1) - 3.6 =2.4 litre
Thus, the ratio of petrol to kerosene = 3.6/2.4 = 3/2
- 8. Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25% copper. Alloys A and B are mixed in the ratio of 1:4 .What is the ratio of gold and silver in the newly formed alloy is?
Options- A. 20% and 30%
- B. 36% and 44%
- C. 25% and 35%
- D. 49% and 36% Discuss
Correct Answer: 36% and 44%
Explanation:
Assume the weight of alloy a is 100 kg
Therefore, The weight of alloy B is 400kg
Gold silver copper
A 40kg 60kg 0kg
B 140kg 160kg 100kg
total 180kg 220kg 100kg
Therefore, Ratio of gold and silver in new alloy = = 36% :44%
- 9. The number of oranges in three baskets are in the ratio of 3 : 4 : 5. In which ratio the no. of oranges in first two baskets must be increased so that the new ratio becomes 5 : 4 : 3?
Options- A. 1:3
- B. 2:1
- C. 3:4
- D. 2:3 Discuss
Correct Answer: 2:1
Explanation:
Let, B1 : B2 : B3 = 3x : 4x : 5x
again B1 : B2 : B3 = 5y : 4y : 3y
Since there is increase in no.of oranges in first two baskets only, it means the no. of oranges remains constant in the third basket
Therefore, 5x = 3y
Hence 3x : 4x : 5x => = 9y:12y:15y
and 5y : 4y : 3y => 25x : 20x : 15x
Therfore, increment in first basket = 16
Increment in second basket = 8
Thus, required ratio = 16/8 = 2:1
- 10. What is the third proportional to 16 and 36 ?
Options- A. 81
- B. 79
- C. 84
- D. 88 Discuss
Correct Answer: 81
Explanation:
f C is the third proportional to A and B, then A/B = B/C If x is the third proportional to 16 and 36, then 16/36 = 36/x => 4/9 = 36/x => x = 36 * 9/4 => x = 9 * 9 => x = 81
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