**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 all**

**oy C.**

(a) 71 2/3%

(b) 28 1/3%

(c) 70 2/3%

(d) 29 1/3%

**1. A**

**(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 **

**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**

**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

**10. C**