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Equations Homework

1. Gopi promises to give Rs. 90000 plus one cycle as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 65000 and the cycle. Find the price of the cycle.
a. Rs. 1500
b. Rs. 2500.
c. Rs. 2000
d. Rs. 1000


2. There are two sections A and B for class X in a a school. If 6 students are sent from A to B, the number of students in B is double that of A. Otherwises, if 12 students from B are sent to A the number of students would be equal in both the sections. Find the number of students in section B initially.
a. 84
b. 78
c. 57
d. 66


3. Mahesh, Pawan, Charan are playing a game of "doubling" and each has some money with them. In each round the looser has to double the money with each of the remaining two players. In the first round, Mahesh lost the game and doubled the money of Pawan and Charan. In the second round Pawan lost and in the third round Charan lost the game. After the third round, they found that each has Rs.120 with them. Find the initial amount with Pawan.
a. 120
b. 115
c. 105
d. 100


4. Bhavya, Divya, Navya, Sravya are best friends. Bhavya has bought "n" chocolates on her birthday. She gives Divya half the number of chocolates plus half chocolate. Then she gives Navya half the remaining number of chocolates plus half chocolate. Finally, she gives half the remaining number of chocolates plus half chocolate. And she left with no chocolates. Then "n" lies in between?
a. \(2 \le n \le 6\)
b. \(5 \le n \le 8\)
c. \(9 \le n \le 12\)
d. \(11 \le n \le 16\)


5. A man spent 1/6th of his life in child hood, 1/12th of his life as youngster and 1/7th of his life as a bachelor. After five years of his marriage a son was born to him. The son died four years before the father died and at the time of his death his age was half the total age of his father. What is the age of the father?
a. 60
b. 72
c. 84
d. 96


6. Pawan has bought a new car. For the car registration, he has the following conditions to be met. The number should be a four digit number having non zero and distinct digits. The sum of digits at the units and tens position is equal to the sum of the remaining two digits. The sum of the digits in the middle positions is three times to the sum of the remaining digits. If the sum of the digits is not more than 20, then how many such four digit numbers are possible.
a. 1
b. 3
c. 6
d. 8


7. Each girl in class 8th has thrice the number of girls as classmates as she has boys as class mates, while Each boy has five times the number of girls as class mates as he has boys as class mates. Total number of students is equal to
a. 13
b. 24
c. 28
d. 42


8. Pawan, Mahesh, Nani, Charan are playing marbles and each has got some marbles. They found that total marbles with them are equal to 100. Also, If you give 4 marbles to Pawan, take away four marbles from Mahesh, multiply Nani's marbles by 4 , divide Charan's marbles by 4 make them equal. Find sum of the marbles with Pawan and Charan.
a. 32
b. 24
c. 72
d. 76


9. In a parking lot there are some cars in some rows. If two more cars are parked in each row, there would be one row less. If three cars are parked in each row then there would be three more rows. The number of cars is
a. 20
b. 40
c. 32
d. 36


10. A student has to divide a number by 7 and add 21 to the quotient. However, being absent minded, he had first added 21 to it and divided it by 7, and got 66 as answer. What is the corrent answer?
a. 84
b. 96
c. 105
d. 112


11. A young girl Roopa leaves home with x flowers, goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the x flowers into the river. The number of flowers doubles. Then she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the third place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand.
If Roopa leaves home with 30 flowers, the number of flowers she offers to each deity is:
a. 30
b. 31
c. 32
d. 33


12. The minimum number of flowers that could be offered to each deity is: (Use data from Question 11)
a. 0
b. 15
c. 16
d. Cannot be determined


13. The minimum number of flowers with which Roopa leaves home is: (Use data from Question 11)
a. 16
b. 15
c. 0
d. Cannot be determined


14. A fraction becomes 4/5 when 1 is added to both the numerator and denominator, and it becomes 5/6 when 6 is added to both the numerator and denominator. The numerator of the given fraction is :
a. 19
b. 21
c. 23
d. 29


15. Katama and Rayudu have some marbles with them. If Katama gave 30 marbles to Rayudu, he would have 40 less than Rayudu. If Rayudu gave 40 marbles to Katama, he would have one third of the marbles with Katama. Find the sum of the marbles with Katama and Rayudu.
a. 150
b. 170
c. 180
d. 200


16. A two digit number when 18 added becomes another two digit number with reversed digits. How many such two digit numbers are possible?
a. 1
b. 2
c. 5
d. 7


17. Ray writes a two digit number. He sees that the number exceeds 4 times the sum of its digits by 3. If the number is increased by 18, the result is the same as the number formed by reversing the digits. Find the sum of the digits of the number.
a. 6
b. 7
c. 8
d. 9


18. A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is
a. 10
b. 12
c. 14
d. 16


19. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.
Which of the following is a valid statement about the cheque amount?
a. Over Rupees 13 but less than Rupees 14
b. Over Rupees 7 but less than Rupees 8
c. Over Rupees 22 but less than Rupees 23
d. Over Rupees 18 but less than Rupees 19

20. Mahesh has x rupees and y paisa in his purse. He spent Rs.8.40 and was left with 2y rupees and 2x paisa. The value of x is...
a. Rs.32
b. Rs.37
c. Rs.41
d. Rs.43