What least number should be added to each term of the ratio 7 ratio 13 to make it to Ratio 3?
Disclaimer Show The questions posted on the site are solely user generated, Doubtnut has no ownership or control over the nature and content of those questions. Doubtnut is not responsible for any discrepancies concerning the duplicity of content over those questions. Rd Sharma 2018 Solutions for Class 7 Math Chapter 9 Ratio And Proportion are provided here with simple step-by-step explanations. These solutions for Ratio And Proportion are extremely popular among Class 7 students for Math Ratio And Proportion Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2018 Book of Class 7 Math Chapter 9 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2018 Solutions. All Rd Sharma 2018 Solutions for class Class 7 Math are prepared by experts and are 100% accurate. Page No 9.10:Question 1:Which ratio is larger in the following pairs? Answer:(i) Writing the ratios as fractions,
we have Page No 9.10:Question 2:Give two equivalent ratios of 6 : 8. Answer:We have Page No 9.10:Question 3:Fill in the following blanks: 1220= 5=9 Answer:1220=
5= 9 Page No 9.13:Question 1:Find which of the following are in proportion? Answer:(i) We have Page No 9.13:Question 2:Find x in the following proportions: Answer:(i) 16 : 18 =
x : 96 Page No 9.14:Question 3:The ratio of the income to the expenditure of a family is 7 : 6. Find the savings if the income is Rs 1400. Answer:The ratio of the income of a family to its expenditure = 7 : 6. Page No 9.14:Question 4:The scale of a map is 1 : 4000000. What is the actual distance between the two towns if they are 5 cm apart on the map? Answer:The scale of the map = 1 : 4000000. Page No 9.14:Question 5:The ratio of income of a person to his savings is 10 : 1. If his savings of one year are Rs 6000, what is his income per month? Answer:Savings in one year = Rs. 6000 Page No 9.14:Question 6:An electric pole casts a shadow of length 20 metres at a time when a tree 6 metres high casts a shadow of length 8 metres. Find the height of the pole. Answer:Length of the shadow of the electric pole = 20 m Page No 9.14:Question 1:Mark the correct alternative in the following question: If a : b = 3 : 4, then 4a : 3b = (a) 4 : 3 (b) 3 : 4 (c) 1 : 1 (d) None of these Answer:As, a:b=3:4⇒ab=34So, 4a:3b=4a3b=43×ab=43×34 =1212=11=1:1 Hence, the correct alternative is option (c). Page No 9.14:Question 2:Mark the correct alternative in the following question: 112: 160= (a) 4 : 1 (b) 1 : 4 (c) 5 : 1 (d) 1 : 5 Answer:Since, 112:160=112÷160=112×601=6012 =51=5:1 Hence, the correct alternative is option (c). Page No 9.14:Question 3:Mark the correct alternative in the following question: The simplest form of 24 : 36 is (a) 9 : 4 (b) 4 : 9 (c) 3 : 2 (d) 2 : 3 Answer:As, 24:36=2436=2 3=2:3So, the simplest form of 24:36=2:3. Hence, the correct alternative is option (d) Page No 9.14:Question 4:Mark the correct alternative in the following question: If a : b = 4 : 5 and b : c = 2 : 3, then a : c = (a) 4 : 3 (b) 8 : 15 (c) 8 : 9 (d) 5 : 3 Answer:As, a:b=4:5⇒ab=45Also, b:c =2:3⇒bc=23So, a:c=ac=abbc=ab×bc=45×23=815=8:15 Hence, the correct alternative is option (b). Page No 9.14:Question 5:Mark the correct alternative in the following question: If p:q=2:5, then 25p+14q5p+7q=a 8:5 b 5:8 c 8:3 d 3:8 Answer:As, p:q=2:5⇒pq=25Let p=2x and q=5xNow , 25p+14q5p+7q=25×2x+14×5x5×2x+7×5x= 50x+70x10x+35x=120x45x=83=8:3 Hence, the correct alternative is option (c). Page No 9.14:Question 6:Mark the correct alternative in the following question: A ratio equivalent to 2 : 5 is (a) 6 : 15 (b) 4 : 5 (c) 5 : 2 (d) 5 : 4 Answer:Since, 2:5=25=2×35×3=615=6:15 So, the ratio equivalent to 2 : 5 is 6 : 15. Hence, the correct alternative is option (a). Page No 9.14:Question 7:Mark the correct alternative in the following question: lf 2a = 3b = 4c, then a : b : c = (a) 2 : 3 : 4 (b) 3 : 4 : 6 (c) 4 : 3 : 2 (d) 6 : 4 : 3 Answer:As, 2a=3b=4c⇒2a=3b and 3b=4c⇒ab=32 and bc=43⇒ab=64 and bc=43⇒a:b=6:4 and b:c=4:3∴ a:b:c=6:4:3 Hence, the correct alternative is option (d). Page No 9.14:Question 8:Mark the correct alternative in the following question: If 2x = 3y and 4y = 5z, then x : z = (a) 4 : 3 (b) 8 : 15 (c) 3 : 4 (d) 15 : 8 Answer:As, 2x=3y⇒xy=32And, 4y=5z⇒yz=54Now, x:z=xz=x yyz=xy×yz=32×54=158=15:8 Hence, the correct alternative is option (d). Page No 9.15:Question 9:Mark the correct alternative in the following question: If a2=b3=c4, then a:b:c=a 2:3:4 b 4:3:2 c 3:2:4 d None of these Answer:As, a2=b3=c4⇒a2=b3 and b3=c4⇒3a=2b and 4b=3c By cross multiplication⇒ab=23 and bc=34⇒a:b=2: 3 and b:c=3:4∴ a:b:c=2:3:4 Hence, the correct alternative is option (a). Page No 9.15:Question 10:Mark the correct alternative in the following question: If 1a:1b:1c=3:4:5, then a:b:c=a 5:4:3 b 20:15:12 c 9:12:15 d 12:15:20 Answer:As, 1a:1b:1c=3:4:5⇒1a:1b=3:4 and 1b :1c=4:5⇒1a÷1b=34 and 1b÷1c=45⇒1a ×b1=34 and 1b×c1=45⇒ba=34 and cb=4 5⇒ab=43 and bc=54 Reciprocal of both sides⇒ab=4×53×5 and bc=5×34×3 ⇒ab=2015 and bc=1512⇒a:b=20:15 and b:c=15:12 ∴ a:b:c=20:15:12 Hence, the correct alternative is option (b). Page No 9.15:Question 11:Mark the correct alternative in the following question: If a : b = 5 : 7 and b : c = 6 : 11, then a : b : c = (a) 35 : 49 : 66 (b) 30 : 42 : 77 (c) 30 : 42 :55 (d) None of these Answer:As, a:b=5:7 and b:c=6:11⇒ab=57 and bc=611 ⇒ab=5×67×6 and bc=6×711×7⇒ab=3042 and bc=4277⇒a:b=30:42 and b:c=42:77∴ a:b:c=30:42: 77 Hence, the correct alternative is option (b). Page No 9.15:Question 12:Mark the correct alternative in the following question: If x:y=1:1, then 3x+4y5x +6y=a 711 b 1711 c 1723 d 45 Answer:As, x:y= 1:1⇒xy=11⇒x=yNow,3x+4y5x+6y =3x+4x5x+6x As, x=y=7x11x=711 Hence, the correct alternative is option (a). Page No 9.15:Question 13:Mark the correct alternative in the following question: If a:b =2:5, then 3a+2b4a+b=a 1613 b 1316 c 2522 d 2021 Answer:As, a:b=2:5⇒ab=25Let a=2x and b=5x. Then,3a+2b4a+b=3×2x+2×5x4× 2x+5x=6x+10x8x+5x=16x13x=1613 Hence, the correct alternative is option (a). Page No 9.15:Question 14:Mark the correct alternative in the following question: The mean proportional of a and b is 10 and the value of a is four times the value of b. The value of a + b (a > 0, b > 0) is (a) 20 (b) 25 (c) 101 (d) 29 Answer:Since, the mean proportional of two positive numbers a and b is the positive number x such that ax=xb.⇒a10=10b⇒ab=100But a=4b ⇒4b×b=100⇒b2=1004⇒b2=25⇒b=25⇒b=5⇒a=4×5=20∴ a+b=20+5=25 Hence, the correct alternative is option (b). Page No 9.15:Question 15:Mark the correct alternative in the following question: If 8 : x : : 16 : 35, then x = (a) 35 (b) 70 (c) 352 (d) 24 Answer:As, 8:x::16:35⇒8x=1635⇒ 16x=8×35 By cross multiplication⇒x=8× 3516 Transposing 16 to RHS∴ x=352 Hence, the correct alternative is option (c). Page No 9.15:Question 16:Mark the correct alternative in the following question: The mean proportional of 6 and 24 is (a) 15 (b) 12 (c) 8 (d) 144 Answer:Let x be the mean proportional of 6 and 24 . Then,6x=x24⇒x2=6×24 By cross multiplication⇒x2=144⇒x=144∴ x=12 So, the mean proportional of 6 and 24 is 12. Hence, the correct alternative is option (b). Page No 9.15:
Question 17:Mark the correct alternative in the following question: The boys and girls in a school are in the ratio 9 : 5. If the number of girls is 320, then the total strength of the school is (a) 840 (b) 896 (c) 920 (d) 576 Answer:Let the number of boys in the school be x.Since, the ratio of boys and girls in the school=9:5⇒Number of boys Number of girls=95⇒x320=95⇒5x=320×9⇒x=320×9 5⇒x=64×9⇒x=576∴ The total strength of the school=576+320 =896 Hence, the correct alternative is option (b). Page No 9.15:Question 18:Mark the correct alternative in the following question: If the first three terms of a proportion are 3, 5 and 21, respectively, then its fourth term is (a) 21 (b) 35 (c) 15 (d) None of these Answer:Let the fourth term be x.As, 3:5::21:x⇒35=21x⇒3x=21×5⇒x =21×53⇒x=7×5∴ x=35 So, the fourth term is 35. Hence, the correct alternative is option (b). Page No 9.15:Question 19:Mark the correct alternative in the following question: What must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3? (a) 5 (b) 3 (c) 4 (d) 6 Answer:Let the number that must be added to each term of the ratio 9:16 be x. Then,9+x:16+x=2:3⇒9+x16+x=23 ⇒39+x=216+x⇒27+3x=32+2x⇒3x-2x=32-27∴ x=5 So, 5 must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3. Hence, the correct alternative is option (a). Page No 9.15:Question 20:Mark the correct alternative in the following question: What least number is to be subtracted from each term of the ratio 15 : 19 to make the ratio 3 : 4? (a) 3 (b) 5 (c) 6 (d) 9 Answer:Let the least number that is to be subtracted from each term of the ratio 15:19 be x. Then,15-x:19-x=3:4⇒15-x19- x=34⇒415-x=319-x⇒60-4x=57-3x⇒3x- 4x=57-60⇒-x=-3∴ x=3 So, 3 is the least number to be subtracted from each term of the ratio 15 : 19 to make the ratio 3 : 4. Hence, the correct alternative is option (a). Page No 9.15:Question 21:Mark the correct alternative in the following question: If ₹840 is divided between P and Q in the ratio 3 : 4, then P's share is (a) ₹340 (b) ₹480 (c) ₹360 (d) ₹400 Answer:Let P's share be ₹x. Then,Q's share=₹840-xAs, P's share:Q's share=3:4⇒P's shareQ's share=34⇒x840-x =34⇒4x=3840-x⇒4x=3×840-3x⇒4x+3x=3×840 ⇒7x=3×840⇒x=3×8407⇒x=3×120∴ x=360 So, P's share is ₹360. Hence, the correct alternative is option (c). Page No 9.15:Question 22:Mark the correct alternative in the following question: The ages of Ravish and Shikha are in the ratio 3 : 8. Six years hence, their ages will be in the ratio 4 : 9. The present age of Ravish is (a) 18 years (b) 15 years (c) 12 years (d) 21 years Answer:Let the present age of Ravish and Shikha be 3x and 8x, respectively.After six years,Age of Ravish =3x+6 years andAge of Shikha=8x+6 yearsSince, 3x +6:8x+6=4:9⇒3x+68x+6=49⇒93x +6=48x+6⇒27x+54=32x+24⇒27x-32x=24-54⇒-5x= -30⇒x=-30-5⇒x=6∴ 3x=3×6=18 So, the present age of Ravish is 18 years. Hence, the correct alternative is option (a). Page No 9.15:Question 23:Mark the correct alternative in the following question: The present ages of Renu and Ravi are in the ratio 5 : 6. The sum of their present ages is 44 in years. The difference of their ages (in years) is (a) 4 (b) 5 (c) 8 (d) 2 Answer:Let the present ages of Renu and Ravi be 5x and 6x.As, the sum of their present ages=44 years⇒5x+6x=44⇒11x=44⇒x=4411∴ x=4 Now, the present age of Renu=5×4=20 years andthe present ages of Ravi=6×4= 24 yearsSo, the difference of their ages=24-20=4 years Hence, the correct alternative is option (a). Page No 9.16:Question 24:
Mark the correct alternative in the following question: The third proportional of 3 and 27 is (a) 243 (b) 256 (c) 289 (d) 225 Answer:Let the third proportional of 3 and 27 be x. Then,3:27: :27:x⇒3:27=27:x⇒327=27x⇒3x=27×27⇒x=27× 273⇒x=27×9∴ x=243 So, the third proportional of 3 and 27 is 243. Hence, the correct alternative is option (a). Page No 9.6:Question 1:If x : y = 3 : 5, find the ratio 3x + 4y : 8x + 5y. Answer:It is given that Page No 9.6:Question 2:If x : y = 8 : 9, find the ratio (7x − 4y) : 3x + 2y. Answer:It is given that Page No 9.6:Question 3:If two numbers are in the ratio 6 : 13 and their l.c.m. is 312, find the numbers. Answer:Let the two numbers be 'x' and 'y' such that x : y = 6 : 13 ⇒ xy = 613
. Page No 9.6:Question 4:Two numbers are in the ratio 3 : 5. If 8 is added to each number, the ratio becomes 2 : 3. Find the numbers. Answer:Let the two numbers in ratio be x and y such that Page No 9.6:Question 5:What should be added to each term of the ratio 7 : 13 so that the ratio becomes 2 : 3 Answer:Let the numbers that must be added to the ratio 7 : 13 be 'x'. Page No 9.6:Question 6:Three numbers are in the ratio 2 : 3 : 5 and the sum of these numbers is 800. Find the numbers. Answer:We have Page No 9.6:Question 7:The ages of two persons are in the ratio 5 : 7. Eighteen years ago their ages were in the ratio 8 : 13. Find their present ages. Answer:Let the present ages of the two persons be '5x' and '7x' years. Page No 9.6:Question 8:Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. Find the numbers. Answer:Let the two numbers be 'x' and 'y'. Page No 9.6:Question 9:Two numbers are in the ratio 2 : 7. If the sum of the numbers is 810, find the numbers. Answer:We have Page No 9.6:Question 10:Divide Rs 1350 between Ravish and Shikha in the ratio 2 : 3. Answer:We have Page No 9.6:Question 11:Divide Rs 2000 among P, Q, R in the ratio 2 : 3 : 5. Answer:We have Page No 9.6:Question 12:The boys and the girls in a school are in the ratio 7 : 4. If total strength of the school be 550, find the number of boys and girls. Answer:We have the ratio boys : girls = 7 : 4. Page No 9.6:Question 13:The ratio of monthly income to the savings of a family is 7 : 2. If the savings be of Rs 500, find the income and expenditure. Answer:We have the ratio of income : savings = 7 : 2. Page No 9.6:Question 14:The sides of a triangle are in the ratio 1 : 2 : 3. If the perimeter is 36 cm, find its sides. Answer:We have the ratio of the sides of the triangle = 1 : 2 : 3. Page No 9.7:Question 15:A sum of Rs 5500 is to be divided between Raman and Aman in the ratio 2 : 3. How much will each get? Answer:We have Page No 9.7:Question 16:The ratio of zinc and copper in an alloy is 7 : 9. If the weight of the copper in the alloy is 11.7 kg, find the weight of the zinc in the alloy. Answer:We have Page No 9.7:Question 17:In the ratio 7 : 8, if the consequent is 40, what is the antecedent? Answer:In a ratio a : b, 'a' is known as the antecedent and 'b' is known as the consequent. Page No 9.7:Question 18:Divide Rs 351 into two parts such that one may be to the other as 2 : 7. Answer:We have Page No 9.7:Question 19:Find the ratio of the price of pencil to that of ball pen, if pencils cost Rs 16 per score and ball pens cost Rs 8.40 per dozen. Answer:We have Page No 9.7:Question 20:In a class, one out of every six students fails. If there are 42 students in the class, how many pass? Answer:We have View NCERT Solutions for all chapters of Class 7 What must added to each terms of the ratio 7 13 so that the ratio becomes 2 3?So, 5 must be added to each term of the ratio 7:13, so that the ratio becomes 2:3.
What is the ratio of 7 13?Ratio of 7 to 13 (7:13) A ratio of 7 to 13 can be written as 7 to 13, 7:13, or 7/13. Furthermore, 7 and 13 can be the quantity or measurement of anything, such as students, fruit, weights, heights, speed and so on.
What must be added to the ratio 7 13?Answer: The number that should be added to each term of 7:13 to make it 2:3 is 5.
What must be subtracted from each term of the ratio 3/7 so that the ratio become 2 5?Therefore, if 1/3 is subtracted from each term of the ratio 3:7, the ratio becomes 2:5.
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