Ratio and Proportion problems
- 1. In a mixture of 60 litres, the ratio of milk and water is 2 : 1. What amount of water must be added to make the ratio 1 : 2?
Options- A. 42 litres
- B. 56 litres
- C. 60 litres
- D. 77 litres Discuss
Correct Answer: 60 litres
Explanation:
Milk = 60 x (2/3) litres =40 litres
Water = (60 - 40) litres = 20 litres
? 40 / (20 + x) = 1/2
? 20 + x = 80
? x = 60
Hence water to be added = 60 litres.
- 2. A sum of Rs. 1300 is divided between A, B and C and D such that ( A's share / B's share ) = ( B's share / C's share ) = ( C's share / D's share ) = 2 / 3, Then A's share is?
Options- A. Rs. 140
- B. Rs. 160
- C. Rs. 240
- D. Rs. 320 Discuss
Correct Answer: Rs. 160
Explanation:
? A : B = 2 : 3, B : C = 2 : 3 and C:D = 2 : 3
? A : B = 8 : 12, B : C = 12 : 18 and C : D = 18 : 27
? A : B : C : D =8 : 12 : 18 : 27
So A's share = Rs. 1300 x ( 8 / 65) = Rs. 160
- 3. Two equals glasses are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents mixed in a tumbler, The ratio of milk and water in the tumbler is?
Options- A. 7 : 5
- B. 7 : 17
- C. 3 : 7
- D. 11 : 23 Discuss
Correct Answer: 7 : 17
Explanation:
First glass contains milk = 1/3 and water = 2/3
Second glass contains milk = 1/4 and water = 3/4
? Now tumbler contains water = (3/2 + 3/4) = 17/12
? Ratio of milk and water =7/12 : 17/12 =7 : 17
- 4. If a : b = c : d then, (ma + nc) / (mb + nd) is equal to?
Options- A. m : n
- B. na : mb
- C. a : b
- D. md : nc Discuss
Correct Answer: a : b
Explanation:
Let (a/b) = (c/d) = k
Then, a = bk and c = dk.
? (ma + nc) / (mb + nd) = (mbk + ndk) / (mb + nd) = k(mb + nd/mb + nd)
= k = a/b = a : b.
- 5. A mixture contains milks and water in the ratio 5 : 1. On adding 5 litres of water the ratio of milk and water becomes 5 : 2. The quantity of milk in the mixture is?
Options- A. 16 litres
- B. 25 litres
- C. 32.5 litres
- D. 22.75 litres Discuss
Correct Answer: 25 litres
Explanation:
Let quantity of milk and water be 5x and x litres.
Then, 5x / (x + 5) = 5/2
? 10x = 5x + 25
? x =5
? Quantity of milk = 5x =25 litres
- 6. A's money is to B's money as 4 : 5 and B's money is to c's money as 2 : 3. If A has Rs. 800, C has?
Options- A. Rs. 1000
- B. Rs. 1200
- C. Rs. 1500
- D. Rs. 2000 Discuss
Correct Answer: Rs. 1500
Explanation:
A : B = 4 : 5 = 8 : 10 and B : C = 2 : 3 = 10 : 15
? A : B : C = 8 : 10 :15
If A has Rs. 8, C has Rs. 15
If A has Rs. 800 C has Rs. (15/8 x 100) = Rs. 1500
- 7. 15 litres of a mixture contains 20% alcohol and the rest water. If 3 litres of water be mixed in it. The percentage of alcohol in the new mixture will be?
Options- A. 17
- B. 162/ 3
- C. 181/ 2
- D. 15 Discuss
Correct Answer: 162/ 3
Explanation:
Alcohol = (20/100) x 15 litres = 3 litres,
Water = 12 litres
New mix, contains,
Alcohol = 3 litres,
Water = 15 litres
? Percentage of alcohol in new mix. = (3/18) x 100 % = 162/ 3%
- 8. Vinay got thrice as many marks in Maths as in English. The proportion of this marks in Maths and History is 4 : 3. If his total marks in Maths, English And History are 250. What are his marks in English?
Options- A. 120
- B. 90
- C. 40
- D. 80 Discuss
Correct Answer: 40
Explanation:
M = 3E and M/H = 4/3
? H = 3/4 M = 3/4 x 3E = 9/4 E
Now M + E + H = 250
? 3E + E + 9/4 E = 250
? 25 E = 1000
? E = 40
- 9. Gold is 19 times as heavy as water and copper 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water is?
Options- A. 1 : 2
- B. 2 : 3
- C. 3 : 2
- D. 19 : 135 Discuss
Correct Answer: 3 : 2
Explanation:
Let, 1 gm of gold be mixed with y gm of copper to give (1 +x) gm of mixture.
Now, 1G =19W and 1C = 9W and mixture = 15W
Now, 1 gm gold + y gm copper = (1 + y) gm mixture
? 19 W + 9W x y = (1 + y ) x 15W
Thus 4W = 6W x y
? y = 4W/6W = 4/6 = 2/3
So the required ratio is 1 : 2/3 i.e. 3 : 2
- 10. Divide Rs. 600 among A, B and C so that Rs. 40 more than 2/5th of A's share,Rs. 20 more than 2/7th of B's share and Rs. 10 more than 9/17th of C's share may all be equal. What is A's share?
Options- A. Rs. 280
- B. Rs. 150
- C. Rs. 170
- D. Rs. 200 Discuss
Correct Answer: Rs. 150
Explanation:
? 2A/5 + 40 = 2B/7 + 20 = 9C/17 + 10 = k
? A = 5(k - 40)/2, B =7(k - 20)/2 and C = 17(k - 10)/9
? 5(k - 40)/2 +7(k - 20)/2 +17/(k - 10 )/9 = 600
? 45k - 1800 + 63k - 1260 + 34k - 340 = 10800
? 142k = 14200
? k = 14200 / 142 = 100
Hence A's share = (5/2) x ( 100 - 40) = Rs. 150
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