Mixture and allegations quiz 1

SP = 1.50 Rs. Profit = 25%. CP = 1.50 x (100/125) = 1.20Rs.

Therefore required ratio = 4 : 5

Explanations



Ratio of Milk to water will be= 18:6,
In 18 litre milk water added = 6 litre
In 1 litre milk water added = 6 / 18
In 36 litre milk water added = (6/18) x 36 = 12 litres

Explanations

Cost price of mixture = (44/110) x 100 = 40 

∴ sugar of 50 paisa per kg to be mixed = (3/5) x 25 = 15kg

Explanations Ratio in which tea and sugar should be mixed = 20 – 13 : 13 – 9.5 = 7 : 3.5 ⇒ 7 : 3.5 ⇒ 2:1 . Let x be quantity at 9.5/kg. ∴ 2 : 1 = x : 17,hence x = 34 kg.

Explanations

1st mixture contains 5 % salt. 2nd mixture contains 75 % water i.e. 25 % salt.
Required % of salt = 18 %. ∴ Required ratio = 25 – 18 : 18 – 5 = 7 : 13 and required price of the mixture = 7.82 – x : x – 7.62 = 7 : 13 ⇒ x = 7.75/ liter. Hence price of 5 liters of this mixture = 7.75 x 5 = Rs. 38.75.

Explanations SP = 60. Gain= 20%. CP = (100/120) x 60. ∴ CP = 50. Ratio between the 2 varieties of custard powder = 60 – 50 : 50 –42 = 10 : 8. ∴ if x is the required quantity then 10 : 8 = x : 16 ⇒ x =20 kg.

Explanations Let the total mixture be x liters. It contains 20 % spirit i.e.0.2 of the total mixture. When 5 liters are drawn off, quantity of spirit removed = 0.2(5) = 1 liters. Remaining spirit = 0.2x –1. Also remaining spirit = 0.12x. ∴ 0.2x - 1 = 0.12x ⇒ x = 12.5L.

Explanations Ratio in which coffee and chicory should be mixed = 12 – 7.5 : 7.5 – 5 = 4.5 : 2.5 ⇒ 9 : 5. Let x be quantity at 4/kg. ∴ 9 : 5 = x : 20 ⇒ x = 36kg.

Sol : Option 3
First alloy – 65% copper. ∴ 35% Nickel. Ratio is 65 : 35
⇒ 13 : 7. 2nd alloy – Ratio is 17 : 3 ∴ Proportion of copper in the 1st alloy = 13/20 and proportion of copper in the 2nd alloy = 17/20.
Also proportion of copper in resulting alloy = 4/5. Hence required ratio is (17/20 – 4/5) : (4/5 – 13/20) = 1 : 3

Sol : Option 1
Let the cask holds x liters of wine. 5 liters of wine is replaced with water.
This operation is done 2 times. ∴ [(x - 5) / x]² = 16 / (16+9)
⇒ [(x - 5) / x]² = 16 / 25
⇒ [(x - 5) / x] = 4/5 ⇒ x = 25 liters