1. Mr X spends 20% of his monthly income on household expenditure. Out of the remaining 25% he spends on children’s education, 15% on transport, 15% on medicine and 10% on entertainment. He is left with Rs. 9800 after incurring all these expenditures. What is his monthly income?
Answer:
Let Mr X monthly income be Rs. 100
Then, money spent on household expenditure =100×20/100 = Rs. 20
? Remaining amount = 100 - 20 = Rs. 80
Money spent on children’s education =80×25/100 = Rs. 20
Money spent on transport =80×15/100 = Rs. 12 Money spent on medicine =80×15/100 = Rs. 12 Money spent on entertainment =80×10/100 = Rs. 8
? Last remaining amount = 100 - (20 + 20 + 12 + 12 + 8) = 100 - 72 = Rs. 28 Now, Rs. 28 is left, when total income is Rs. 100
Rs. 1 is left, when total income =100/28
? Rs. 9800 is left, when total income =100/28×9800 = Rs. 35000
2. kg of an alloy A is mixed with 8 kg of alloy B. If alloy A has lead and tin the ratio 1 : 3 and B has tin and copper in the ratio 2 : 3, then what is the amount of tin in the new alloy?
Answer:
Quantity of tin in alloy A = 6 × (3/4) = 4:5 kg
Quantity of tin in alloy B = 8 × (2/5) = 3.2kg
Quantity of tin in the new alloy = 4 . 5 + 3.2 =7.7 kg
3. A shopkeeper buys an article at a discount of 20% on the listed price from a wholesaler. The shopkeeper marks up the price by 15% on the listed price. A buyer pays Rs.3795 to get it after paying sales tax at the rate of 10% on the price asked for. Find the profit percentage of the shopkeeper.
Answer:
Let the listed price = Rs. 100
CP of shopkeeper = 100 – 20 = Rs. 80
Marked price by shop keeper = 100 + 15 = Rs. 115 Now, 115 = 3795 x (100/110) = 3450
80 = (3450/115) × 80 = Rs. 2400
CP of shopkeeper = Rs. 2400 Profit = 3450 - 3400 = 1050
Profit % = (1050 / 2400) x100 = 43.75%
4. A bought a certain quantity of banan as at a total cost of Rs. 1500. He sold 1/3 of these bananas at 25% loss. If he earns an overall profit of 10%, at what percentage profit did A sell the rest of the bananas?
Answer:
Total CP = 1500
Total SP = 1500 + 10% of 1500 = 1500 + 150 = 1650
CP of 1/3 of bananas = 1500/3 = Rs.500
SP of 1/3 of bananas at 25% loss = 500 – [ (500 x25 / 100)] = 500 - 125 = 375
SP of the rest of bananas = 1650 - 375 = 1275
Now, CP of the test of bananas = 1500 - 500 = 1000
Profit on the rest of bananas = 1275 -1000 = 275
% of profit on the rest of bananas = (275/1000)×100 = 27.5%
5. Two friends A and B simultaneously start running around a circular track . They run in the same direction. A travels at 8 m/s and B runs at b m/s. If they cross each other at exactly three points on the circular track and b is a natural number less than 20, how many values can b take?
Answer:
Let track length be equal to T.
Time taken to meet for the first time = T/relative speed=T/8-b or T/b-8
Time taken for a lap for A = T/8
Time taken for a lap for B = T/b
So, time taken to meet for the first time at the starting point = LCM (T/8,T/b)=T/HCF(8,b)
Number of meeting points on the track = Time taken to meet at starting point/Time taken for first meeting = Relative speed / HCF (8,b.
(8-b)/HCF(8,b) = 3 or (b-8)/HCF(8,b) = 3
b = 2, 5, 11,14 satisfy this equation. So, there are four different values that b can take.
6. If a five digit number is formed with digits 1,2,3,4 and 5.What is the probability that it will be divisible by 25,if repetition is not allowed?
Answer:
Last two digits must be 25
Therefore first three digits can be arranged in 3! Ways and total number =5!
Hence=3!/5!=1/20
7. I bought 3pen,4pencil and 7 eraser that costed me Rs 83,then I bought 2pen,1 pencil and 3 eraser nd that costed me Rs 17.If I have to buy 2 pen, 2 pencil and 4 eraser how much do I need to pay?
Answer:
3pen+4Pencil+7eraser=83
2pen+1pencil+3eraser=17
On adding 5pen+5pencil+10 eraser=100
Pen+pencil+2eraser=20
8. Two pipes can fill a tank in 28 and 24 minutes respectively and a waste pipe can empty 5 gallons per min ute. All three pipes working together can fill the tank in 16 minutes. How much time is taken by the waste pipe to empty the full tank?
Answer:
Let the capacity of the tank be 336 litres
LMC of (28, 24 and 16 = 336)
Waste pipe empties the tank in (12 + 14 - 21) 5 litres per minute
Waste pipe empties the tank in (336/5) = 67.2 minutes
9. C can do 1/4 of a work in 80 days, D can do 40% of the same work in 80 days and E can do 1/3 of a work in 800/3 days. Who will complete the work first?
Answer:
Time taken to complete the work by C=80×4=320 days
Time taken to complete the work by
D=80×100/40=200 days
Time taken to complete the work by E=800/3×3=800 days
10. 49 pumps can empty a reservoir in 17/2 days working 6 hours a day. If 119 pumps are used for 7 hours a day then in how many days will the same work be completed?
Answer:
Let the required number of days be x.
49 x (17/2) x 6 = 119 x 7 x x
x = 3 days
11. At present, the ratio of the ages of A to B is 3 : 8; and that of A to C is 1 : 4. Three years ago, the sum of the ages of A, B and C was 83 years. What is the present age (in years) of C?
Answer:
According to the question, A : B = 3 : 8
A : C = 1 : 4
B : A = 8 : 3
A : C = 1 : 4
8 : 3 : 12
Sum = 8x + 3x 12x = 23x
Now, 23x = 92
x = 4
Hence the present age of C = 12x = 12 x 4 = 48 years
12. Rohit borrowed Rs. 6000 at 5% p.a. simple interest for 2 years. After that he invests it in a scheme which offers 7 ¼% p.a for 2 years. Find the profit of Rohit in the transaction per year.
Answer:
Profit in 2 years = [6000 × 29/4 × 2/100 – 6000 × 5 × 2/100] = 870 – 600 = Rs 270
So profit per year = 270/2 = Rs 135
13. A cyclist, cycling on a road, passes a man who was walking at the rate of 4 km/hr in the same direction. The man could see the cycle for 12 min and it was visible to him up to a distance of 1.2 km. What was the speed of the cycle?
Answer:
Let the speed of cycle be x km/h. Speed of man = 4 km/h
Relative speed = (x-4) km/h Therefore, (x-4)×12/60= 1.2
x – 4 = 6
x = 10 km/h
14. Two shops A and B marked the same brand of jeans for Rs.900. Shop A offers successive discounts of 15% and 15% While shop B offers successive discounts of 20% and 10%. Then the difference in the selling price of jeans is?
Answer:
Final selling price of jeans in shop A = (900- 900×0.15)- (900-900×0.15)×0.15 = Rs. 650.25 Final selling price of jeans in shop B = (900-900×0.20)- (900-900×0.20)×0.10= Rs.648 Difference = Rs.2.25
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