Skip to main contentSkip to question navigationSkip to solution

IPMAT Indore 2019 (MCQ) PYQs

View all IPMAT/JIPMAT PYQs →
Collection of AfterBoards IPMAT JIPMAT Past Year Papers with Solutions

IPMAT Indore 2019

Arithmetic
>
Mixture & Alligation

Hard

An alloy PP has copper and zinc in the proportion of 5:25:2 (by weight), while another alloy QQ has the same metals in the proportion of 3:43:4 (by weight). If these two alloys are mixed in the proportion of a:ba:b (by weight), a new alloy RR is formed, which has equal contents of copper and zinc. Then, the proportion of copper and zinc in the alloy SS, formed by mixing the two alloys PP and QQ in the proportion of b:ab:a (by weight) is

✅ Correct Option: 3
Understanding the given information:
Alloy PP: Copper : Zinc = 5:25:2 (by weight)
Alloy QQ: Copper : Zinc = 3:43:4 (by weight)
Alloy RR: Made by mixing PP and QQ in ratio a:ba:b, has equal copper and zinc
Alloy SS: Made by mixing PP and QQ in ratio b:ab:a
Finding the fraction of copper in each alloy:
In Alloy PP: Total parts = 5+2=75 + 2 = 7
Copper fraction = 57\dfrac{5}{7}
In Alloy QQ: Total parts = 3+4=73 + 4 = 7
Copper fraction = 37\dfrac{3}{7}
Setting up equation for Alloy RR:
When mixing PP and QQ in ratio a:ba:b, copper fraction in mixture:
a×57+b×37a+b\dfrac{a \times \dfrac{5}{7} + b \times \dfrac{3}{7}}{a + b}
Since RR has equal copper and zinc, copper fraction = 12\dfrac{1}{2}
a×57+b×37a+b=12\dfrac{a \times \dfrac{5}{7} + b \times \dfrac{3}{7}}{a + b} = \dfrac{1}{2}
Solving for ratio a:ba:b:
Cross multiplying:
a×57+b×37=12(a+b)a \times \dfrac{5}{7} + b \times \dfrac{3}{7} = \dfrac{1}{2}(a + b)
Multiplying by 1414:
10a+6b=7a+7b10a + 6b = 7a + 7b
3a=b3a = b
Therefore: a:b=1:3a:b = 1:3
Finding composition of Alloy SS:
Alloy SS mixes PP and QQ in ratio b:a=3:1b:a = 3:1
Copper fraction in SS:
3×57+1×373+1=157+374=1874=1828=914\dfrac{3 \times \dfrac{5}{7} + 1 \times \dfrac{3}{7}}{3 + 1} = \dfrac{\dfrac{15}{7} + \dfrac{3}{7}}{4} = \dfrac{\dfrac{18}{7}}{4} = \dfrac{18}{28} = \dfrac{9}{14}
Zinc fraction in SS:
1−914=5141 - \dfrac{9}{14} = \dfrac{5}{14}
Copper : Zinc = 914:514=9:5\dfrac{9}{14} : \dfrac{5}{14} = 9:5
The proportion of copper and zinc in alloy SS is 9:59:5

Related questions:

IPMAT Indore 2020

Fifty litres of a mixture of milk and water contains 30 percent of water. This mixture is added to eighty litres of another mixture of milk and water that contains 20 percent of water. Then, how many litres of water should be added to the resulting mixture to obtain a final mixture that contains 25 percent of water?

IPMAT Indore 2022

In a room, there are nn persons whose average height is 160 cm160 \ \text{cm}. If mm more persons, whose average height is 172 cm172 \ \text{cm}, enter the room, then the average height of all persons in the room becomes 164 cm164 \ \text{cm}. Then m:nm: n is

IPMAT Indore 2022

In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question