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31. Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18 : 10 : 12 and if the wages of an individual man, woman and child is in ratio 6 : 5 : 3, then how much a woman earn in a day?

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Solution:
Ratio of number of men, women and children,
=186:105:123=3:2:4
Total (Men + Women + Children) = 18
3X + 2X + 4X = 18
9X = 18
X = 2
Hence, number of women = 2X = 2 × 2 = 4
Share of all women = 10×400040  = Rs. 1000 [18 + 10 + 12 = 40]
Thus, share of each woman = 10004 = Rs. 250
32. A and B are two alloys in which ratios of gold and copper are 5 : 3 and 5 : 11 respectively. If these equally amount of two alloys are melted and made alloy C. What will be the ratio of gold and copper in alloy C?

Discuss
Solution:
Ratio of Gold and Copper in Alloy A = 5 : 3
Ratio of Gold and Copper in Alloy B = 5 : 11
Amount of Gold in Alloy A = 58
Amount of Gold In Alloy B = 516
Amount of Copper in A = 38
Amount of Copper in B = 1116
Amount of Gold In C,
= (Amount of gold in A + Amount of gold in B) = 58 + 516 = 10+516 = 1516
Amount of Copper in C,
= Amount of Copper in A + Amount of Copper in B = 38 + 1116 = 1716
So,
Ratio of Gold and Copper in C,
=1516:1716=15:17
33. A bag contains an equal number of one rupee, 50 paise and 25 paise coins. If the total value is Rs. 35, how many coins of each type are there?

Discuss
Solution:
Let X coins of each type of there
Total Value = Rs. 35
Now,
X + X2 + X4 = 35
4X + 2X + X = 140
7X = 140
X = 20
34. A bucket contains a mixture of two liquids A and B in the proportion 7 : 5. If 9 litres of mixture is replaced by 9 liters of liquid B, then the ratio of the two liquids becomes 7 : 9. How much of the liquid A was there in the bucket ?

Discuss
Solution:
Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively.When 9 litres of mixture are drawn off, quantity of A in mixture left:
=[7x−712×9]litres=[7x−214]litresSimilarly quantity of B in mixture left,=[5x−512×9]litres=[5x−154]litres∴ratio becomes,7x−214(5x−154)+9=79⇒28x−2120x+21=79⇒252x−189=140x+147⇒112x=336⇒x=3So the can contained,=7×x=7×3=21litres of A initially.
35. A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B, then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket?

Discuss
Solution:

Let bucket contains 5x and 3x of liquids A and B respectively.
When 16 litres of mixture are drawn off, quantity of A in mixture left:
5x−58×16=5x−10Similarly quantity of B in mixture left,3x−38×16=3x−6Now the ratio becomes,5x−103x−6=35⇒25x−50=9x−18⇒16x=32⇒x=2So, quantity of liquid B initially,=3×2=6litres

36. 8 litres are drawn from a cask filled with wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the total solution is 16 : 81. How much wine did the cask hold originally?

Discuss
Solution:
Let the quantity of the wine in the cask originally be x litres.
Using formula:
Final Amount of solute that is not replaced =Initial Amount × (Vol. after removalVol. after replacing)N
Where N = No. of operation done.
Then ratio of wine to total solution in cask after 4 operations,
1×(x−8x)4=1681⇒1×{x−8x}4=(23)4⇒x−8x=23⇒3x−24=2x⇒x=24litres
37. The milk and water in a mixture are in the ratio 7 : 5. When 15 liters of water are added to it, the ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is:

Discuss
Solution:
Milk   :   Water
7 : 5
7 : 8
    3 unit

∴ Remember water is added and not milk, so make milk equal but here milk is already equal
3 units = 15 litres
1 units = 5 litres
8 units = 40 litres
Total quantity of water in the new mixture = 40 litres
38. If x : y = 5 : 2, then (8x + 9y) : (8x + 2y) is :

Discuss
Solution:
xy=52
Means x = 5, y = 2
Putting value of x and y in expression
8 × 5 + 9 × 2 = 58
8 × 5 + 2 × 2 = 44
58 : 44 = 29 : 22

39. Tom is chasing Jerry. In the same interval of time Tom jumps 8 times while Jerry jumps 6 times. But the distance covered by Tom in 7 Jumps is equal to the distance covered by Jerry in 5 Jumps. The ratio of speed of Tom and Jerry is:

Discuss
Solution:
Given;
7 jumps of Tom = 5 jumps of Jerry
Or, TomJerry=57
Let Jerry's 1 leap = 7 meter and Tom's 1 leap = 5 meter
Then, ratio of speed of Tom and Jerry
= 8×56×7
= 4042
= 20 : 21
40. The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond ?

Discuss
Solution:
Ratio of Ducks and Frogs in Pond = 37 : 39
Average of Ducks and Frogs in Pond = 152
So, total number of Ducks and Frogs in the Pond = 2 × 152 = 304
∴ Number of Frogs = 304×3976  = 156

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