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QUESTION: 1

What is the angle in degrees made by a sector, the ratio of whose area with the area of the semicircle is equal to 1:10?

Solution:

QUESTION: 2

The value of a diamond varies directly as the square of its weight. If a diamond worth Rs 10,000 is divided into 2 pieces in the ratio of 4:6, what is the loss in value?

Solution:

QUESTION: 3

The first, second and third class fares between two railway stations, Patna and Lucknow were 10:8:3 and the number of first, second and third class passengers between the two stations was is 3:4:10. If total sales of the ticket is Rs 16,100, find the money obtained by the sales of second class tickets.

Solution:

Let the fare of 1st, 2nd and 3rd class be lOx, 8x, and 3x respectively and let the no. of passengers of 1st, 2nd and 3rd class be 3y, 4y and lOy respectively, then 30xy + 32xy + 30xy = 16100 ⇒ 92xy = 16100 Hence xy = 175

Required amount = 32xy = 32 x 175 = 5600

QUESTION: 4

Two horses cost as much as 5 dogs, 6 dogs as much as 8 oxen, 10 oxen as much as 50 sheep, 14 sheep as much as 9 goats. If the price of one goat is Rs 70, how much will one horse cost?

Solution:

QUESTION: 5

A is proportional to B. B is inversely proportional to C. C is proportional to the square of D. D is directly proportional to the cube root of E. Assuming positive integers, if A increases then E

Solution:

QUESTION: 6

The sum of four numbers is 233. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?

Solution:

QUESTION: 7

Arun has a certain amount of money in the denomination of 1 rupee and 10 rupee notes . T he number of 1 rupee notes multiplied by the number of 10 rupee notes is equal to the total money (in rupees) that he has. What is the total number of ten rupee notes that he can have?

Solution:

Let x = no. of Re 1 notes and y = no. of Rs 10 notes So, xy = x+ 10y ⇒xy = x + 10y Now, go through options

QUESTION: 8

Three friends A, B and C started a venture with capitals in the ratio of 4:1:15. At the end of every quarter A halves his capital, while B doubles his capital and C leaves his capital untouched. This process is repeated till the end of the year. If at the end of the year B ’ s share of the profit is Rs 22,000, what is the total profit?

Solution:

QUESTION: 9

Gandhiji owns cows, some black and some white. He finds that 4 black cows and 3 white cows gave the same amount of milk in 5 days as 3 black cows and 5 white cows gave in 4 days. What is the ratio of milk given by a black cow in a day to that given by a white cow in a day?

Solution:

Let 1 black cow gives x litres milk in 1 day and 1 white cow gives y litres milk in 1 day. Then 5(4.x + 3y) = 4(3x + 5y) ⇒ 20x + 15y = 12x + 20y

QUESTION: 10

A metal trader buys 2 kinds of silver foils, the ratio of their prices being 1:4. He sells the alloy at Rs 90 per kg so that he can make a profit of 20%. If the ratio of their quantities present in a alloy is 6:1 respectively, find the purchase price of the foil present in lesser quantity.

Solution:

QUESTION: 11

Read the passage below and solve the questions based on it.

A book having pages between 4,000 and 5,000 is divided into four pans, each part being divided into chapters The total number of pages in each of the four parts is the same. The ratio of the chapters across all the parts is 6:5:10:14. The number of chapters in the fourth part is 70

Q.

What is the total number of pages in the book?

Solution:

Let the no. of chapters be 6x, 5x, lOx and 14x.

Also, 14x = 70, x = 5 Thus, chapters are 30, 25, 50 and 70.

We can easily eliminate (a) as no. of pages has to be in between 4000 and 5000.

For (b) Each parts well have 1200 pages which is not possible for part having 70 chapters. Only option (c) satisfies the conditions.

QUESTION: 12

The ratio of the age of Sita and her mother is 2:3. N years from now, ratio of their ages will become 3:5. What is the value of N?

Solution:

QUESTION: 13

P works twice as fast as Q, whereas P and Q together can work three times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?

Solution:

If P is taking 3 days to do some work, then Q takes 6 days to do the same work. Now, both of them will take 2 days to complete the work. So, R takes 6 days to complete the same work.

Hence, earning should be distributed in the ratio of their efficiency, i.e., 2 : 1 : 1.

QUESTION: 14

Read the passage below and solve the questions based on it.

There are certain number of apples, guavas and oranges in a basket. The number of each variety is more than one. The ratio of the number of apples to the number of guavas is equal to the ratio of the number of guavas lo the number of oranges.

Q.

If the total number of fruits is 61, then find the number of guavas.

Solution:

Number of apples/Number of guavas = Number of guavas/Number of oranges (Number of guavas)2 = Number of apples x Number of oranges This gives us a hint that Number of apples x Number of oranges should be a prefect square.

Now start using the options.

Option (b) satisfies the relationship (16/20 = 20/25)

QUESTION: 15

Anand and Bhavana have a few one rupee, 50 paise and 25 paise coins each. The total amount with each of them is Rs 5. The number of coins of two of the three types of coins that Anand has are equal and same is the case for the coins that Bhavana has. If Anand has the maximum possible total number of coins, then find the maximum possible total number of coins that Bhavana can have given that she has fewer coins than Anand.

Solution:

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