1. In what ratio milk with 40% concentration is mixed with another milk with concentration 60% to get 55% concentration?
a. 2 : 3
b. 1 : 3
c. 3 : 1
d. 3 : 2

Answer: B

Explanation:

$\therefore$ The quantities are mixed in the ratio $5:15$ or $1 : 3$

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2. In what ratio must alcohol with 50% concentration mixed with water so that the resultant mixture has concentration 20%?
a. 2 : 3
b. 3 : 2
c. 4 : 5
d. 5 : 4

Answer: A

Explanation:
Here water concentration = $0\%$

$\therefore$ Alcohol and water are to be mixed in $20 : 30$ or $2 : 3$
$A = \dfrac{{mx + ny}}{{m + n}}$
Here, $A$ = target average $m,\; n$ = quantities $x,\;y$ = averages
In the given question, 5, 15 are quantities, 40%, and 60% are averages.
Resultant concentration = $A$ $ = \dfrac{{mx + ny}}{{m + n}}$ $ = \dfrac{{5 \times 40 + 15 \times 60}}{{5 + 15}}$ $ = \dfrac{{1100}}{{20}} = 55\%$

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3. In what ratio Sugar costing Rs.15 per kg be mixed with sugar costing Rs.24 per kg so that the mixture is worth Rs.20 per kg?
a. 4 : 5
b. 2 : 3
c. 3 : 1
d. 1 : 3

Answer: A

Explanation:

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4. A shopkeeper sold some quantity at a loss of 5% and rest at 12% profit, making 8% profit on the whole. Find the ratio between the goods he sold at loss and profit.
a. 4 : 13
b. 5 : 13
c. 13 : 4
d. 5 : 12

Answer: A

Explanation:
Here averages are $-5$ and $+12$ for loss and profit.

$\therefore$ Required ratio = $4 : 13$

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5. A total sum of Rs.130 was collected for a small party from boys and girls of a team of 5. If each boy contributes Rs.20 and each girl contributes Rs.30. Find the number of girls in that team.
a. 1
b. 2
c. 3
d. 4

Answer: C

Explanation:
Average contribution by each student $ = \dfrac{{130}}{5} = 26$

Total girls in the team $ = \dfrac{6}{{6 + 4}} \times 5 = 3$

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6. A person invested Rs.5000 in two schemes which offer interest rates 10% p.a and 15% p.a respectively. If he gets a total of Rs.600 as interest, find the money invested at first scheme.
a. Rs.3000
b. Rs.1500
c. Rs.1000
d. Rs.800