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### Answers :-

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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