Page 181 - classs 6 a_Neat

EXAMPIE:5 Are 20. 18. 5, 6 in proportion? 2. Which of the following ratios are in proportion?
SOLUTION We have: 20:18 = 20 = 10 ⋅ and,5:6 = 5 ⋅ a.4, 7,5, 9 b.5, 25,6, 30 c. 21, 7,81, 9 d. 15,40, 3,8 e.8, 15, 5, 9
18 9 6 3. Write the given three numbers in continued proportion.
∴ 20 : 18 ≠ 1; 5 : 6. a. 3, 9,27 b. 12, 36,108 C. 2,8, 32 d. 10, 15, 20 e.4,6,9
Hence, 20, 18, 5, 6 are not in proportion. 4. Find the mean proportion of the following.
Alternative method Product of extremes= (20 × 6) = 120. a.9,81 b.5,45 C. 4, 16 d.4, 100 e. 12,48
Product of means= (18 × 5) = 90. 5. Find the value of x in the following questions given that the three number are in continued proportion.
∴ product of extremes -:1; product of means. a. x, 8 and 64 b.25, x and 4 c. 36, x, 49
Hence, 20, 18, 5, 6 are not in proportion. d.6, 18,x e. 4, 20 and x
EXAMPLE:6 if 36 : 81 : : x : 63.find the value of ×. 6. A gardener plants 16 trees in 4 hours. How many trees will he plant in 6 hours?
SOLUTION Clearly, product of means = product of extremes. 7.In a hostel canteen, 10 kg of sugar is sanctioned for 21 students in a week. How much sugar will be required
36 63 for 441 students?
×
×
∴ 81 x×= 36 63 ⇒ x = 28. 8. The cost of 15 watches is ₹75,000. What will be the cost of 28 watches?
81 9. A car travels 165 km in 3 hours. How long will it take to travel 3J_Q km, if it is moving at a constant speed?
Hence, x = 28. 10. A carpenter makes 54 tables in 18 days. In how many days can he make 24 tables working at the same rate?
EXAMPLE: If 36: x:: x: 16,jlnd the value of x.
Solution Clearly, product of means = product of extremes. SOLVED EXAMPLES
∴ x×x=36 × l6 ⇒ x =(6×6)x(4×4)=(6×4) =(24)2
2
2
⇒x = 24. EXAMPLE:1 If 15 oranges cost t 70, what is the cost of 39 oranges?
Hence, x = 24. SOLUTION Cost of 15 oranges = t 70.
THREE NUMBERS IN PROPORTION Cost of 1 orange = ₹   70   [less oranges. less cost].
Three numbers a, b, c are said to be in proportion if a, b, b, c are in proportion.  15 
∴ a, b, c are in proportion  70 

⇒ a, b, b, care in proportion Cost of 39 oranges= ₹   15 × 39 = ₹ 182 [more oranges, more cost].

⇒ a:b::b:c
⇒b =ac, Hence, the cost of 39 oranges is t 182.
2
EXAMPLE: 8 if 25, 35, x are in proportion.find the value of x. EXAMPLE 2. A truck runs 492 km on 36 L of diesel. How many kilometres can it run on 33
SOLUTION 25, 35, x are in proportion L of diesel?
⇒ 25, 35, 35, x are in proportion SOLUTION Distance covered on 36 L of diesel = 492 km.
⇒ 25 : 35 : : 35 : x Distance covered on 1 L of diesel =   492   km [less diesel, less distance ].
⇒ 25 xx= 35 x 35 [product of extremes = product of means]  36 
35 35
×

⇒ x = = 49. Distance covered on 33 L of diesel =  492 × 33 km = 451 km
25   36  
Hence, x = 49.
[more diesel, more distance].
JUST TRY :1 Find x,where 3:x :: 4:12.
JUST TRY :2 if 10, 20 and care in continued proportion, find the third proportion or c. EXAMPLE 3. Hence, on 33 L of diesel the truck can run 451 km.
25 bags of wheat, each weighing 50 kg, cost ₹10000. Find the cost of 35 bags of
JUST TRY :3 Find the mean proportion of the following numbers: 5, 20.
JUST TRY :4 The cost of one dozen pencils is t60. How much will 75 pencils cost? wheat each weighing 40 kg.
JUST TRY :5 Roh it drives his car at a constant speed of 50 km/hr. How long does he take SOLUTION Total weight of 25 bags of 50 kg each= (50 × 25) kg= 1250 kg.
Total weight of 35 bags of 40 kg each = ( 40 × 35) kg = 1400 kg.
Cost of 1250 kg of wheat=₹ 10000.
EXERCISE 13-B
Cost of 1 kg of wheat =₹   10000   [less wheat, less cost].
1. Fill in the blanks so that the four terms are in proportion.  1250 
a. :4 :: 32:16 f. 9:12 :: :8 Cost of 1400 kg of wheat= ₹  10000 1400 [more wheat more cost]

b. 5 :: 15:25 g. 8:20 :: 16:   1250 ×  
c.18: :: 10:5 h.5:7 :: 35: = ₹11200.
d. 30: :: 24:12 i. :36 :: 4:12 Hence, the cost of 35 bags of 40 kg each is ₹11200.
e. 7:15 :: :3o f:105 :: :15