Ratio and Proportion problems
- 1. A sum of ? 7000 is divided among A, B, and C in such a way that the shares of A and B are in the ratio 2 : 3 and those of B and C are in the ratio 4 : 5, The ahare of B is
Options- A. ? 1600
- B. ? 2000
- C. ? 2400
- D. ? 3000 Discuss
Correct Answer: ? 2400
Explanation:
Given, A : B = 2 : 3
and B : C = 4 : 5
Then, A : B : C = 8 : 12 : 15
7there4; Share of B = [12/(8 + 12 + 15)] x 7000
= (12 x 7000)/35
= 2400
= ? 2400
- 2. A sum of money is divided among A, B, C and D in the ratio of 3 : 7 : 9 : 13 . If the share of B is ?, then what will be the total amount of money of A and C together?
Options- A. ? 8352
- B. ? 6998
- C. ? 9784
- D. ? 7456 Discuss
Correct Answer: ? 8352
Explanation:
Let A's share = 3N
B's share = 9N
and D's share = 13N
According to the question
7N = 4872
? N = 4872/7 = 696
Share of A and C = 3N + 9N = 12N
= 12 x 696 = ? 8352
- 3. The ratio between the ages of A and B is 3 : 5 and the sum of their ages is 56 yr. The ratio between their ages 7 yr ago was
Options- A. 3 : 4
- B. 3 : 5
- C. 1 : 2
- D. 2 : 3 Discuss
Correct Answer: 1 : 2
Explanation:
Age of A = (3/8) x 56 = 21 yr
Age of B = (5/8) x 56 = 35 yr
Before 7yr, ration of the ages of A and B
= (21 - 7) : (35 - 7)
= 14 : 28
= 1 : 2
- 4. The ratio of the ages of a father to that of their ages (in years) is 1000, then find the father's age after 10 yr.
Options- A. 50 yr
- B. 60 yr
- C. 80 yr
- D. 100 yr Discuss
Correct Answer: 60 yr
Explanation:
Let the age of father = 5k
and the age of son = 2k
According to the question,
5k x 2k = 1000
? 10k2 = 1000
? k2 = 100
? k = ?100 = 10
? Father's age after 10 yr = (5k + 10)
= 5 x 10 + 10
= 60 yr
- 5. 35% of a number is two times 75% of another number. What is the ratio between the first and the second number, respectively?
Options- A. 35 : 6
- B. 31 : 7
- C. 23 : 7
- D. 32 : 9 Discuss
Correct Answer:
Explanation:
Let first number is P and second number is Q.
Then, according to the question,
P x 35% = 2 x Q x 75%
? (P x 35)/100 = (2 x Q x 75)/100
? P/Q = (2 x 75)/35 = (2 x 15)/7 = 30/7
? P : Q = 30 : 7
- 6. The ratio of milk and water in 85 kg of adulterated milk is 27 : 7. The amount of water which must be added to make the ratio 3 : 1 is?
Options- A. 5 kg
- B. 6.5 kg
- C. 7.25 kg
- D. 8 kg Discuss
Correct Answer: 5 kg
Explanation:
Milk = 85 x (27/34) kg = 135/2 kg = 67.5 kg
Water = 85 x (7/34) kg = 35/2 kg = 17.5 kg
Let Amount of water to be added is x,
? 67.5 / (17.5 + x) = 3/1
? 3 (17.5 + x) = 67.5
? x =5
? Water to be added = 5 kg.
- 7. Rs. 1870 has been divided into three parts in such away that half of the first parts, one-third of the second parts, and one-sixth of the third parts are equals. The third parts is?
Options- A. Rs. 510
- B. Rs. 680
- C. Rs. 850
- D. Rs. 1020 Discuss
Correct Answer: Rs. 1020
Explanation:
1/2A = 1/3B =1/6C = x
? A = 2x, B = 3x, C =6x
? A : B : C = 2 : 3 : 6
Third part = Rs. (1870 x 6/11) = Rs. 1020
- 8. In a town 80% of the population are adults of which the men and women are in the ratio of 9 : 7, respectively. If the number of adult women is 4.2 lakh, what is the total population of the town?
Options- A. 12 lakh
- B. 9.6 lakh
- C. 9.8 lakh
- D. 11.6 lakh Discuss
Correct Answer: 12 lakh
Explanation:
let the number of adult men be N.
Then, ratio of the numbers of adult men and adult women
9 : 7 = N : 4.2
? N = (9/7) x 4.2 = 5.4 Lakh
Total adult population = 4.2 + 5.4 = 9.6 lakh.
If the population of the town be M Lakh,
then, 80M/100 = 9.6
? M = (9.6 x 100)/80 = 12 lakh
- 9. Mr. Shrimant inherits 2505 gold coins and divides them among his three sons, Bharat, Parat and Marat, in a certain ratio. Out of the total coins received by each of them, Bharat sells 30 coins Parat donates his 30 coins and Marat losses 25 coins. Now the ratio of gold coins with them is 46 : 41 : 34, respectively. How many coin did Parat receive from his father?
Options- A. 705
- B. 950
- C. 800
- D. 850 Discuss
Correct Answer: 850
Explanation:
According to the question.
(46k +30) + (41k + 30) + (34k + 25) = 2505
? 121k = 2505 - 85 = 2420
? k = 2420/121 = 20
? Number of coins received by Parat = 41k + 30
= 41 x 20 + 30 = 850
- 10. ? 600 are divided among A, B and C such that ? 40 more then 2/5th of A's share, ? 20 more then 2/7 th of B's Share and ? 10 more then 9/17 th of C's share, all are equal. What is B's share?
Options- A. ? 150
- B. ? 185
- C. ? 280
- D. ? 285 Discuss
Correct Answer: ? 280
Explanation:
2A/5 + 40 = 2B/7 + 20 = 9C/17 + 10 = K
Then, A = (5/2) x (K - 40), B = (7/2) x (K - 20), C = (17/9) x (K - 10)
According to the question, A + B + C = 600
? (5/2) x ( K - 40) + (7/2) x (K - 20) + (17/9) x (K - 10) = 600
? 45 x (K - 40 ) + 63 x (K - 20) + 34 x (K - 10) = 10800
? 45K - 1800 + 63K - 1260 + 34K - 340 = 10800
? 142K - 3400 = 10800
? 142K = 10800 + 3400
? 142K = 14200
? K = 14200/142 =100
? B = (7/2) x (K - 20) = (7/2) x (100 - 20)
= (7 x 80)/2 = 7 x 40
= ? 280
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