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Q1MULTIPLE CHOICE
A milkman dilutes 36 litres of milk with water. The percentage of milk in the solution is now 80%. How many litres of water does he add?
Answer: B
Original milk contains 100% milk. Water contains 0% milk.
Resultant mixture contains 80% milk.
∴ Using Alligation, we are mixing a liquid with 100% milk with another liquid with 0% milk to give a liquid that has 80% milk.
∴ Ratio of Milk and Water = 80 : 20 = 4 : 1
∴ If there are 36 litres of milk
∴ 4 : 1 = 36 : x
∴ x = 9
Hence, option (b).
Q2MULTIPLE CHOICE
How much chicory at Rs. 40 a kg should be added to 15 kg of tea at Rs. 100 a kg, so as to make the mixture worth Rs. 65 a kg?
Answer: B
∴ Required ratio of quantity of chicory and tea = 7 : 5
∴ Amount of Chocory / Amount of Tea = 7 / 5
∴ Amount of Chicory = 7/5 × 15 = 21 kg
Hence, option (b).
Q3TYPE IN THE ANSWER
Aakash invested some part of Rs 5,00,000/- in stock X and the remaining part in stock Y. At the end of the year, Stock X gave a return of 42% and Stock Y gave a return of 37%. Aakash’s total interest earnings from his investment in both the stocks was Rs 2,00,000/-. How much did he invest in stock Y?
Answer: 200000
Total earnings of Rs 2,00,000/- is 40% of 5,00,000.
So, ratio of investments in X to that of Y is 3 : 2.
Hence investment in Y is 2/5th of Rs. 5,00,000 = Rs 2,00,000.
Hence, 200000.
Q4TYPE IN THE ANSWER
Solution 1 has 52% milk. Solution 2 has 40% milk. 15 litres from the first Solution is poured into a 3rd container. What quantity (in litres) from Solution 2 should be added to the 3rd container to get a resultant solution of 44% milk?
Answer: 30
Let ‘x’ litres be the quantity of the mixture in Solution 2.
Therefore, 4/8 = 15/x
Therefore, x = 30 litres.
Hence, 30.
Q5MULTIPLE CHOICE
A dealer mixes cereal costing Rs. 8 per kg with cereal costing Rs. 7 per kg and sells the mixture at Rs. 8 per kg and earns a profit of on his sale price. In what proportion does he mix them.
Answer: B
Selling Price of the mixture = Rs. 8/kg
7.5% profit is earned on selling price, hence profit = Rs. 8 × 7.5% = Rs. 0.6
∴ CP of the mixture = 8 - 0.6 = Rs. 7.4
∴ Ratio = 0.4 : 0.6 = 2 : 3
Hence, option (b).
Q6TYPE IN THE ANSWER
A 24 kg ingot contains 54% gold. Another 12 kg ingot contains 72% gold. Both these are melted together to form a new 36 kg ingot. What will be the percentage of gold in the new ingot?
Answer: 60
Let ‘x’ be the percentage of gold in the new ingot. Therefore, using rule of allegation.
Therefore,
That gives, X = 60%
Alternately,
It would be better to use the weighted average approach here.
i.e. weighted average (X) =
⇒ X = = 2 × 18 + 24 = 60%.
Hence, 60.
Q7MULTIPLE CHOICE
The average monthly salary of employees, consisting of officers and workers, of an organisation is Rs. 3000. The average salary of an officer is 10,000 while that of a worker is 2000 per month. If there are total 480 employees in the organisation, find the number of officers.
Answer: A
Ratio of officers to workers = 1000 : 7000 = 1 : 7
Number of officers = 1/8 × 480 = 60
Alternately,
Let the number of officers be x
Number of workers = 400 – x
⇒ 10000 × x + 2000(400 - x) =3000(400)
⇒ 10000x + 800000 - 2000x = 12,00,000
⇒ 4x = 600 - 400 = 200
⇒ x = 50
∴ Number of officers = 50
Hence, option (a).
Q8MULTIPLE CHOICE
What amounts (in litres) of 90% and 97% pure acid solutions respectively are mixed to obtain 35 L of 95% pure acid solution?
Answer: D
∴ Amount of the solution x and y in ratio 2 : 5
Amount of 90% acid in solution x = 2/7 × 35 = 10L
Amount of acid in solution y = 5/7 × 35 = 25L
Hence, option (d).
Q9MULTIPLE CHOICE
A trader has 100 kg of rice, part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4%. How much quantity is sold at 14% profit and that at 6% loss?
Answer: A
Hence, ratio of quantity sold at 14% profit and 6% loss = 2 : 18 = 1 : 9
Hence, rice sold at 14% profit = (100 × 1)/10 = 10 kg
Rice sold at 6% loss = 90 kg.
Hence, option (a).
Q10MULTIPLE CHOICE
In a zoo, there are Rabbits and Pigeons. If heads are counted, there are 400 and if legs are counted, there are 1120. How many pigeons are there?
Answer: D
Heads Count = 400.
Legs count = 1120.
Average Legs count for per head = 1120/400 = 14/5.
