   ### Percentage And Time - I ( 5 min module )

FOR BANKS & CLERICAL EXAMS PREPARATION
PERCENTAGE & TIME - I
If a store has an \$100 item, marks it 20% off, then charges 6% sales tax, what is the final price ?
First, calculate 20% of \$100. That's 0.20 × \$100 or \$20. We then subtract that \$20 from the original price of \$100 to get a reduced sale price of \$80.
Now we add in the sales tax. Here's where the tricky part comes in; what is the base ? That is, do we pay 6% tax on the original \$100 price or on the reduced \$80 price ? In most places, we would pay tax on the reduced sales price, so \$80 is the base. Thus, we multiply \$80 × 0.06 to get \$4.80 and add that to \$80 to get \$84.80 for a final price.
Notice that even though we took off 20% and then added back in 6%, this is not the same as taking off 14%, since the 20% and the 6% figures each had a different base. If the 6% sales tax did apply to the original full price, however, then both percentages would have the same base and the total reduction in price would, indeed, be 14%, bring the price down from \$100 to \$86.
If your clock goes slow, you can be late to office.
REMEMBER
• If you take 20% off an amount (or a 20% reduction), that means the new price is 20% less than the original (100%) price, so it's now 80% of the original price.
• If you apply 20% interest to an amount, that means the new price is 20% higher than the original (100%) price, or 120% of the original price. (Note that this is simple interest, we will consider compound interest next.)
• When the minute hand moves by 1 hour or 360°, the hour hand will also move by 30° further. Obviously the hour hand is not at standstill position.
REVISION TIME
Q1 – Shopping store offers you discount 50% + 40%on discounted price. How much net discount do you get.
Q2 – On an item of Rs. 500, you get flat discount of 50%. But the shopkeeper insist you pay the VAT of 12% on the original price. How much will you pay ?
Q3 – You take a loan of 5000 and the bank charges you 8% per annum compound interest. You return 3000 in the first year, 1500 the 2nd year, 500 the 3rd year & the remaining amount in 4th year. Can you tell how much you will pay in the 4th year to settle your loan?
Q4 – You again take the same loan now and the bank charges simple interest this time. You pay the whole amount after 4 years in lump sum. How much did you pay extra in this question w.r.t above situation?
Q5 – It is exactly 12 O' clock. After how much time will the minute hand and the hour hand meet again?
Q6 – The clock loses 3 seconds every hour. Is the clock going fast or slow ? And after how much time will the clock show the exact right time again ?

Answer – 1 – You are getting first 50% off and then 40% more on the already discounted price.
Means 40%of remaining = 40% of 50% = 0.4 x 0.5 = 0.2 or 20%
Total discount = 50% + 20% =70%
You pay net amount = 30%
Answer – 2 – Discount of flat 50% on 500 = 250
Remaining amount = 250
But VAT is on original amount = 12% of 500 = 60
Net amount you pay = 250 + 60 = 310
Answer – 3-  Loan in first year = 5000 & interest charged =8% on 5000 = 400
Summed up total after 1st year = 5000 + 400 =5400
You pay = 3000
Leftover = 5000 – 3000 = 2000
Interest of 8% on 2000 will be charged in 2nd year = 160
Summed up amount after 2nd year = 2000 + 160 = 2160
You pay next 1500
Leftover = 2160 – 1500 = 660
Interest of 8% is charged on 660 = 52.80
Summed up amount = 660 +52.80 = 712.80
You pay in 3rd year 500 and leftover amount = 712.80 – 500 = 212.80
Interest charged is 8% again on 212.80 = 17.02
You will settle loan by last payment of = 212.80 + 17.02 = 229.82
Answer – 4- For 4 years 8% interest is charged on 5000
= PTR / 100 = 5000 x 4 x 8 /100 = 1600
Net amount required to pay = 1600 + 5000 = 6600
In previous question you have paid = 3000 + 1500 + 500 + 229.82 = 5229.82
Extra amount paid here = 6600 – 5229.82 = 1370.18
When minute hand moves by 360°,
the hour hand will move by  5/60 x 360° = 30°
So angular velocity of minute hand = 360°/60 minutes = 6°/minute
And angular velocity of hour hand = 30°/60 minutes = 0.5°/minute
Relative angular velocity of minute hand w.r.t hour hand = 6-0.5 = 5.5°/minute
In order to catch up the hour hand again, relatively minute hand must complete one full circle = 360°
So time take will be = 360 / 5.5 = 65.45 minutes = 1 hour 5 minutes and 27 seconds
Answer – 6 – If the clock is losing time means it is going fast.
It loses 3 seconds every hour. To catch up exact time again with the right watch. The difference in time must be 12 hours. So what we all need to calculate is in how much time will the clock loose 12 hours or 12 x 3600 sec.
The time required will be 12  x 3600 / 3 = 14400 hours or 60 days