1.Two alloys A and B contain gold and silver in the ratio of 1 : 2 and 1 : 3 respectively. A third alloy C is formed by mixing A and B in the ratio of 2 : 3. Find the percentage of silver in the alloy C.
(a) 71 2/3%
(b) 28 1/3%
(c) 70 2/3%
(d) 29 1/3%
1. A
(Solution)
(Solution)
Alloy A = 300 and B = 300
Let 100 : 200 ( 1 : 2)
75 : 225 (1 : 3)
A = 100 × 2 : 200 × 2
75 × 3 : 225 × 3
425 : 1075
For % =1075/1500×100=215/3=71(2/3%)
2.Two alloy contain silver and copper in the ratio of 2 : 3 and 3 : 4. In what ratio the two alloys should be added together to get a new alloy having silver and copper in the ratio of 1 : 2? Find the percentage of gold in the alloy C.
(a) 41 19/21%
(b) 67 13/21%
(c) 32 5/21
(d) 67 16/21%
2.A (Same as question 1)
3.An amount of Rs. 1250 is distributed among A, B and C in the ratio of 4 : 7 : 14. What is the ratio between the difference of shares of B and A and the difference of shares of C and B ?
(a) 7 : 3
(b) 2 : 7
(c) 3 : 7
(d) 7 : 2
3.C
4.The prices of a scooter and a television set are in the ratio 3 : 2. If a scooter costs Rs. 6000more than the television set, the price of the television set is:
(a) Rs. 18000
(b) Rs. 12000
(c) Rs. 10000
(d) Rs. 6000
4.B
5.The contents of two vessels containing water and milk are in the ratio 3 : 4 and 5 : 4 are mixed in the ratio 1 : 4. The resulting mixture will have water and milk in the ratio_________.
(a) 184 : 176
(b) 167 : 184
(c) 167 : 148
(d) 148. 167
5.C
6.The contents of two vessels containing water and milk are in the ratio 2 : 3 and 4 : 5 are mixed in the ratio 1 : 2. The resulting mixture will have water and milk in the ratio_________.
(a) 77 : 58
(b) 58 : 77
(c) 68 : 77
(d) 77 : 68
6.B
7.The contents of two vessels containing water and milk are in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4. The resulting mixture will have water and milk in the ratio _________.
(a) 31:74
(b) 31:77
(c) 33:74
(d) 33:76
7. A
Solutions
Solutions
Detail Method: Change the ratios into fractions.
Water : Milk
Vessel I 1/3 2/3
Vessel II 2/7 5/7
From Vessel I, I/5 is taken and from Vessel II, 4/5 is taken.
Therefore, the ratio of water to milk in the new vessel =(1/3×1/5+2/7×4/5):(2/3×1/5+5/7×4/7)
=(1/15+8/35):(2/15+20/35)=31/105:74/105=31∶74
Quicker Method: Applying the above theorem, we have,
The required answer = 1×1×(2+5)+4×2(1+2) ∶1×2(2+5)+4×5(1+2)
=1×7+8×3∶2×7+20×3=31∶74
8.Two vessels contain equal quantity of mixtures of milk and water in the ratio 5 : 2 and 6 : 1 respectively. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained.
(a) 11:3
(b) 3:11
(c) 12:4
(d) 5:12
8. A
9.One man adds 3 litres of water to 12 litres of milk and another 4 litres of water to 10 litres of milk. What is the ratio of the strengths of milk in the two mixtures?
(a) 27:26
(b) 24:25
(c) 28:25
(d) 25:45
9. C
Solution
Solution
Strength of milk in the mixture =(Quantity of Milk)/(Total Quantity of Mixture)
∴ Strength of milk in the first mixture =12/(12+3)=12/15
Strength of milk in the second mixture= 10/(10+4)=10/14
∴ The ratio of their strengths =12/15:10/14
=12×14∶15 ×10
=28∶25
10.A bag contains rupee, 50-paise and 25-paise coins in the ratio 3 : 4 : 5. If the total amount in the bag is Rs. 625, find the no. of coins of 25-paise.
(a) 125
(b) 1250
(c) 500
(d) 1000
