Direct and inverse variation
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This document discusses direct and inverse variation. It defines direct variation as a relationship that can be written as y=kx, where k is a constant, and inverse variation as a relationship that can be written as y=k/x, where k is a constant and x is not equal to 0. It provides examples of direct and inverse variation problems and their solutions. It also includes two worksheets with additional problems involving direct and inverse variation and asks the reader to determine the solutions.
Direct and inverse variation
- 1. DIRECT AND INVERSE VARIATION SOMETHING ABOUT DIRECT AND INVERSE VARIATION Variation, in general, will concern two variables; say height and weight of a person, and how, when one of these changes, the other might be expected to change
- 2. TYPES OF VARIATIONS • DIRECT VARIATON A direct variation is an equation that can be written in the form y = kx, where k is a nonzero constant. • INDIRECT Variation A relationship that can be written in the form y = k , where k is a nonzero constant and x ≠ 0, is an inverse variaton x
- 3. SOME EXAMPLES • DIRECT VARIATION • RAMESH BOUGHT 5 STAMPS FOR RS 10 HOW MAY CAN HE BUY FOR RS 10. • WE CAN FIND THE SOLUTION BY FOLLOWING FORMULA - • X = KY THE ANSWER IS 20 X NO.OF STAMPS 5 10 Y COST IN RUPEE 10 X
- 4. • INDIRECT VARIATION • A TRAIN 360M LONG IS RUNNING AT A SPEED OF 45km/hr . HOW MUCH WILL IT TAKE TO CROSS A 140M LONG BRIDGE. • FIRST WE WILL CONVERT THE SPEED INTO M/SEC FROM KM /HR • THAT IS 12.5. THEREFORE WE GET THE ABOVE STATEMENT. • WE CAN FIND THE SOLUTION BY THE FORMULA- • K=XY • THE ANSWER IS 40 SEC DISTANCE (IN M) 12.5 500 TIME (IN SEC) 1 X
- 5. WORKSHEET-1 • If the wages of 12 workers for 5 days are $ 7500, find the wages of 17 workers for 6 days. (a) $ 10943 (b) $ 11057 (c) $ 12750 (d) $ 13473 • If a man earns $ 805 per week, in how many days he will earn $ 1840? (a) 7 days (b) 16 days (c) 19 days (d) 23 days • If car covers 102 km in 6.8 litres of petrol, how much distance will it cover in 24.2 litres of petrol? (a) 363 km (b) 330 km (c) 375 km (d) 396 km • If 8 oranges cost $ 10.40, how many oranges can be bought for $ 33.80? (a) 21 (b) 23 (c) 25 (d) 26 • If 18 dolls cost $ 630, how many dolls can be bought for $ 455? (a) 9 (b) 11 (c) 13 (d) 15 • If 3 persons can weave 168 shawls in 1 4 days, how many shawls will be woven by 8 persons days? (a) 153 (b) 189 (c) 127 (d) 160
- 6. WORKSHEET-2 • 1. If 32 men can reap a field in 15 days, in how many days can 20 men reap the same field? 2. 12 men can dig a pond in 8 days. How many men can dig it in 6 days? 3. A hostel has enough food for 125 students for 16 days. How long will the food last if75 more students join them? 4. 8 taps having the same rate of flow, fill a tank in 27 minutes. If two taps go out of order, how long will the remaining taps take to fill the tank? 5. If 12 men or 15 women can finish a piece of work in 66 days, how long will 24 men and 3 women take to finish the work? 6. 70 patients in a hospital consume 1350 litres of milk in 30 days. At the same rate, how many patient 1710 litres in 28 days?
- 7. WORKSHEET-2 • 1. If 32 men can reap a field in 15 days, in how many days can 20 men reap the same field? 2. 12 men can dig a pond in 8 days. How many men can dig it in 6 days? 3. A hostel has enough food for 125 students for 16 days. How long will the food last if75 more students join them? 4. 8 taps having the same rate of flow, fill a tank in 27 minutes. If two taps go out of order, how long will the remaining taps take to fill the tank? 5. If 12 men or 15 women can finish a piece of work in 66 days, how long will 24 men and 3 women take to finish the work? 6. 70 patients in a hospital consume 1350 litres of milk in 30 days. At the same rate, how many patient 1710 litres in 28 days?