Ques 1.
If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is 25/51 . What is the original fraction?
Solution :
⇒ Numerator increased 150% , So it becomes 100x+150x=250x
⇒ Denominator increased 350%, So it becomes 100y+350y=450y
⇒ (250x)/(450y) = 25/51
⇒ x/y = 15/17
Ques 2.
The ratio of the present ages of Anju and Sandhya is 13: 17. Four years ago the ratio of their ages was 11: 15. What will be the ratio of their ages six years hence?
Solution :
Present ages ratio =13:17
4 years ago ratio. = 11:15
⇒ Check ratios differences
13-11 = 2 ; 17-15 = 2 ( this is used when difference is equal, otherwise we need to convert ratios)
⇒ 2 parts ------- 4years
⇒ 13 parts ------ ?
Anju age = 26 years
2 parts ------- 4 years
17 parts ---- ?
⇒ Sandhya age = 34 years
⇒ After 6 years anju age = 26+6=32
⇒ Sandhya = 34+6 =40
⇒ After 6 years ratio = 32:40 = 4:5
Ques 3.
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
Solution:
Rectangular perimeter = he covered distance in 8 minutes
⇒ 2 (3x+2x) = 12 *8 * 1000/60= 1600
⇒ 10x = 1600
⇒ x = 160
Length = 3x = 3* 160 = 480m
Breadth = 2x = 2 *160= 320m
⇒ Area = lb = 480*320= 153600 sq.m
Ques 4.
15, 25, 40, 65, ?, 195
Solution :
⇒ 15 x 2 = 30 -5 = 25
⇒ 25 x 2 = 50-10=40
⇒ 40 x 2 = 80-15 = 65
⇒ 65 x 2 = 130-20= 110
Ques 5.
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Solution :
⇒ Time taken by "A" = 6days
⇒ Time taken by "B" = 8days
⇒ A,B and C are finished in 3 days
⇒ L.C.M of 6,8 and 3 = 24
⇒ Efficiency of "A" = 24/6 = 4
⇒Efficiency of " B" = 24/8= 3
⇒ Efficiency of "A+B+C" = 24/3 =8
⇒ 4+3+C = 8
⇒ C efficiency = 8-7= 1
Share of C = (1/8) x (3200) = 400
Ques 6.
I. 6x² - 49x+99=0.
II. 5y²+17y+14=0
find relation between X and Y?
Solution :
6x²-49x+99=0
⇒ (3x-11) (2x-9)=0
⇒ x=11/3, 9/2
5²+17y+14
⇒ (5y+7) (y+2)
⇒ y=-2,-7/5
x>y
Ques 7.
In how many different ways can the letters of the word BAKERY be arranged?
Solution :
Total Letters in word = 6
Possibility ways =6! = 720
Ques 8.
A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, find in the water level in the tank?
Solution :
Cylinder volume= πr²h
= 22/7×35/2×35/2×h
= 11000
height = 80/7
Ques 9.
Mohan gave 25% of a certain amount of money to Ram. From the money Ram received, he spent 20% on buying books and 35% on buying a watch. After the mentioned expenses, Ram has rs 2700 remaining. How much did Mohan have initially?
Solution :
25%×45%=2700
100%=2700×100×100/25×45 = 24000
==> Mohan have initially = 24000
Ques 10.
A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres? (revenue per passenger is same)
Solution :
cp=100
sp=120
after reduction
Let the auto requires 1 liter petrol per trip i.e 30rs,
profit per trip = 20*30/100 = 6 rs
Total fare per trip = 30+6=36rs
Fare per passenger = 36/3 = 12 rs
Fare for 4 passengers = 4*12 = 48rs
Profit per trip per liter(for petrol price rs 24) = 48-24= 24
