1.) The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is
a) 25
b) 72
c) 63
d) 36
2.) Ananya has only Re 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Re 1 and Rs 2 coins are, respectively
a) 35 and 15
b) 35 and 20
c) 15 and 35
d) 25 and 25
3.) The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively
a) 4 and 24
b) 5 and 30
c) 6 and 36
d) 3 and 24
4.) Find the value of x and y in the given rectangle.
5.) If x+1 is a factor of 2x3 + ax2 + 2bx + 1, then find the values of a and b given that 2a–3b = 4.
6.) The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.
7.) Two years ago, Muskan was thrice as old as her daughter and six years later, she will be four years older than twice her age. How old are they now?
8.) The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.
9.) Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers.
10.) In a competitive examination, 1 mark is awarded for each correct answer while 1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?
11.) Jamila sold a table and a chair for Rs 1050, thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got Rs 1065. Find the cost price of each.
[Hint : Add and Subtract the final equations to get the simplified form.]
12.) It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled.How long would it take for each pipe to fill the pool separately?
13.) The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box.Find the cost of a pen and a pencil box.
14.) Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and of the bus.
15.) A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in
going 40 km upstream as in going 40 km downstream. Find the speed of the
stream.
16.) A two-digit number is obtained by either multiplying the sum of the digits by 8 and
then subtracting 5 or by multiplying the difference of the digits by 16 and then
adding 3. Find the number.
17.) A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket.
18.) A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.
19.) Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received Rs 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs 20 more as annual interest. How much money did she invest in each scheme?
20.) Vijay had some bananas, and he divided them into two lots A and B. He sold the first lot at the rate of Rs 2 for 3 bananas and the second lot at the rate of Re 1 per banana, and got a total of Rs 400. If he had sold the first lot at the rate of Re 1 per banana, and the second lot at the rate of Rs 4 for 5 bananas, his total collection would have been Rs 460. Find the total number of bananas he had.
1.) D 2.) D 3.) C 4.) x=1 & y = 4 5.) a = 5, b = 2 6.)55° and 85° 7.) 38 years. 14 years. 8.) 40 years 9.) 40, 48 10.) 100 11.) Rs 500, Rs 400 12) 20 hrs and 30 hrs 13.) Rs 10, Rs 15 13.) 14.) 10 km/h, 40 km/h 15.) 2.5 km/h 16.) 83 17.) Rs 2500, Rs 30 18.) Rs 600, Rs 400 19.) Rs 12000, Rs 10000 20.) 500
