Q1. Three members of a family A, B and C, work together to get all household chores done. The time it takes them to do the work together is six hours less than A would have taken working alone, one hour less than B would have taken alone, and half the time C would have taken working alone. How long did it take them to do these chores working together?
(a) 20 minutes
(b) 30 minutes
(c) 40 minutes
(d) 50 minutes
Q2. A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 45% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examination?
Q3. A dealer buys dry fruits at Rs. 100, Rs 80 and Rs. 60 per kilogram. He mixes them in the ratio 4 : 5 : 6 by weight, and sells at a profit of 50%. At what price per kilogram does he sell the dry fruit?
(a) Rs. 116
(b) Rs . 106
(c) Rs. 115
(d) Rs. 112
Q4. A man buys a truck for Rs. 2,50,000. The annual repair cost comes to 2.0% of the price of purchase. Besides, he has to pay an annual tax of Rs. 2000. At what monthly rent must he rent out the truck to get a return of 15% on his net investment of the first year?
(a) Rs. 3350
(b) Rs. 2500
(c) Rs. 4000
(d) Rs. 3212.50
Q5. Prema goes to a shop to buy a sofa set costing Rs. 13,080. The rate of sales tax is 9%. She tells the shopkeeper to reduce the price of the sofa set to such an extent that she has to pay Rs. 13080 inclusive of sales tax. Find the percentage reduction needed in the price of the sofa set to just satisfy her requirement. (rounded off to two decimal places).
Q6. Through an inlet, a tank takes 8 h to get filled up. Due to a leak in the bottom, it takes 2 h more to get it filled completely. If the tank is full, how much time will the leak take to empty it?
(a) 20 h
(b) 24 h
(c) 32 h
(d) 40 h
Q7. The length of a rectangular field is 12 m and its breadth is 5 m. Find the length of the diagonal of a square field having the same area as that of the rectangular field.
(a) 2√30 m
(b) √15 m
(c) 10 m
(d) 2√10 m
Q8. The base of a triangle is 15 cm and height is 12 cm. The height of another triangle of double the area having base 20 cm is:
(a) 10 cm
(b) 18 cm
(c) 19 cm
(d) 20 cm
Q9. A playground is in the shape of a rectangle, A sum of Rs. 1000 was spent to make the ground usable at the rate of 25 paisa per m^2. The breadth of the ground is 50 m. If the length of the ground is increased by 20 m, what will be the expenditure in rupees at the same rate per m^2?
Q10. A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. The area of the circle is [Take π=22/7]
(a) 155 cm^2
(b) 130 cm^2
(c) 500 cm^2
(d) 616 cm^2
Maximum marks for each subject =200/(3×5)×x=40/3 x
Pass marks for each subject =45/100×40/3 x=6x
So, he passed in all 5 subjects
Let he bought 4x kg, 5x kg and 6x kg of dry fruits
Total cost price for dealer =(4x×100)+(5x×80)+(6x×60)
Total selling price for dealer = 1740 x
Required price per kg =1740x/15x=116
Total yearly expenditure for man =250,000+2000+2/100×250,000=257000
Total monthly expenditure for man =257000/12
Required monthly rent =15/100×257000/12=3212.5 Rs
Let the new cost of sofa set = x
Required % reduction =1080/13080×100=8.26%
Sol. Let the leak takes x h to empty the tank,
Now, part filled by inlet in 1h = 1/8
Part filled by (inlet + leak) in 1 h
According to the question,
∴ x = 40 h
Sol. Length of the diagonal =(√(12×5))×√2
Sol. Required height =(2 × 15 × 12)/20
= 18 cm.
Sol. Area of rectangular filed =1000/(1/4)
∴ Length =(4000/50) = 80 m
New length of field = (80 + 20) = 100 m
Area = (100 × 50) = 5000 m^2
∴ Required expenditure
= Rs. (5000×1/4) = Rs. 1250
Sol. 2?r = 2(18 + 26)
⇒ r = 14 cm
∴ Area of circle =πr^2