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Solution :-
1e 2d 3d 4b 5e 6a 7c 8d 9b 10a
1.(5) In 60 gm. of mixture, Quantity of water
= 60 × 75/100 = 45 gm
Quantity of milk = 15 gm
After mixing 15 gm of more water,
Quantity of water in the new mixture = 45 + 15 = 60 gm
∴ Quantity of water in 75 gm of mixture = 60 gm
∴ 100 gm of mixture will contain
= 60/75 × 100 = 80% of water
2.(4) Total weight of the mixture = 40 + 25 = 65 kg
Total cost price of wheat
= Rs. (40 × 12.50 + 25 × 15.10)
= Rs. (500 + 377.50)
= Rs. 877.50
Total selling price of wheat
= Rs. 877.50 × 110/100
= Rs. 965.25
∴ SP per kg = Rs. 965.25/65
= Rs. 14.85
3.(4) C.P. of 40 kg of mixture
= Rs. (25 × 32) + (15 × 36)
= Rs. 800 + 540
= Rs. 1340
S.P = of 40 kg of mixture
= Rs. (40 × 40.2)
= Rs. 1608
Profit = Rs. (1608 – 1340) = Rs. 268
Profit % = 268/1340 × 100 = 20%
4.(2) Remaining mixture in the vessel = 60 litres
Milk = 22/25 × 60 = 52.8 litres
Water = 7.2 litres
On adding additional milk and water,
Milk = 52.8 + 4.8 = 57.6 litres
Water = 7.2 + 4.8 = 12 litres
∴ Requried percent
= 57.6 – 12/57.6 × 100
= 45.6/57.6 × 100
= 475/6
5.(5) Let x litres of milk was taken out firstly.
∴ (120 – x)/23 = 4/1
= 120 – x = 92
= x =120 – 92 = 28 litres
∴ Quantity of milk
= 120 – 28 = 92 litres
Quantity of water = 23 litres
Case II
In 23 litres of mixture,
Milk = 4/5 × 23 = 92/5 litres
Water = 23/5 litres
∴ Remaining milk
= 92 – 92/5 = (460 – 92)/5
= 368/5 litres
Quantity of water
= 23- 23/5 + 27
= (115 – 23 + 135)/5 = 227/5 litres
∴ Required ratio = 368/5 : 227/5
= 368 : 227
6.(1) In Initial mixture of the vessel,
Milk : Water = 80 : 18 = 40 : 9
In 49 litres of mixture,
Milk = 40 litres
Water = 9 litres
Let 2x litres of milk and x litres of water be added.
Let 2x litres of milk and litres of water be added.
According to the question.
(40 + 2x)/(9 + x) = 4/1
= 36 + 4x = 40 + 2x
= 4x – 2x = 40 – 36
= 2x =4
x = 2 litres
7.(3) Initial quantity of mixture in the vessel = x litres
(let)
∴ In the vessel,
Apple Juice = 3x/12 litres
= x/4 litres
Orange juice = 5x / 12 litres
Mango Juice = 4x / 12 = x/3 litres
In 12 litres of mixture,
Apple Juice= 3 litres
Orange juice=5 litres
Mango juice = 4 litres
On adding 8 litres of apple juice,
Apple juice in the vessel
= x/4 – 3 + 8 = (x/4 + 5) litres
According to the question
x/4 + 5 = 5x/12 – 5
= x + 20/4 = (5x – 60)/12
= x + 20 = (5x – 60)/3
= 3x + 60 = 5x – 60
= 5x- 3x = 60 + 60
= 2x = 120
x = 60 litres
8.(4) Total initial quantity of juice in the vessel = 4x+ 6x
+ 5x =
15x litres
In 15 litres of juice,
Grapes’s juice = 4 litres
Pineapple’s juice = 6 litres
Banana juice = 5 litres
According to the question,
(6x – 6 + 2) – (4x – 4 + 8) = 10
= 6x – 4 – 4x – 4 = 10
=2x – 8 = 10
= 2x = 10 + 8 = 18
= x = 9
∴ Intial quantity of mixture = 15x
= 15 × 9 = 135 litres
9.(2) In 20 litres of mixture
Milk = 3/5 × 20 = 12 litres
Water = 8 litres
In 10 litres of mixture,
Milk = 6 litres
Water = 4 litres
On adding 10 litres of milk,
Milk = 12 – 6 + 10 = 16 litres
Water = 8 – 4 = 4 litres
Again,in 10 litres of mixture,
Milk =4/5 × 10 = 8 litres
Water = 2 litres
On adding 10 litres of milk,
Milk = 16 – 8 + 10 = 18 litres
Water = 2 litres
Required ratio = 18 : 2
= 9 : 1
10.(1) Remaining quantity of milk
= Initial quantity
= (1 – Quantity taken out/Initial quantity)n
60[1(12/60)]2
= 60 (1 – 1/5)2 = 60 (4/5)2
= (60 × 4 × 4)/(5 × 5)= 38.4 litres
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