NCTB Class 7 Math Chapter Two Exercise 2.1 Solution by Math Expert. Bangladesh Board Class 7 Math Solution Chapter 2”Proportion, Profit & Loss” Exercise 2.1 Solution.

Board |
NCTB |

Class |
7 |

Subject |
Math |

Chapter |
2 |

Chapter Name |
”Proportion, Profit & Loss” |

Exercise |
2.1Solution |

**Exercise:- 2.1**

** Solution:- **(i) (a) 3 kg : 6 kg : : 5TK : 10TK.

= 3 : 6 : : 5: 10

(b) 9 year: 18 year : : 10 day : 20 day

= 9: 18 : : 10 : 20

(c) 7 cm: 28 cm : : 15 second : 1 min (60 second)

= 7: 128: : 15 : 60

(d) 12 note books: 15 pencil : : TK20: TK 25

= 12: 15 : : 20: 25

(e) 125 boys : 25 teachers : : TK. 2500: TK. 500

= 125: 25 : : 2500: 500

**(2) Two marginal quantities of the continued proportion are given below. Form the proportion:**

Solution:- (a) 6, 24

Let, the middle no is x.

Therefore, 6: x : : x : 24

=> x = 6X 24

=> x^{2} = 144

= √12

Therefore, Proportion= 6: 12 : : 24.

**(b) 25:81**

Let, the middle number is x.

Therefore, 25: x : : x: 81

=> x = 25×81

=> x^{2} = V25x81

= 5×9

= 45

Therefore, Proportion = 25: 45 : : 45:81

**(c) 16:49**

Let, middle number is x.

16:x : : x: 49

=> x = 16×49

=> x^{2} = √16×49

= 4×7

= 28

Therefore, Proportion= 16: 28 : : 28: 49.

**(d) 5/7, 1- 2/5**

= 5/7, 7/5

Let, middle number is ‘x’

Therefore, x = 5/7 x 7/5

=> x = √1

= 1

Proportion is, 5/7: 1 : : 1: 7/5.

**(e) 1.5, 13.5**

Let, middle number, x.

Therefore, x= 1.5x 13.5

=> x^{2} = 20.25

=> x^{2} = √20.25

= 4.5

Therefore, Proportion is, 1.5: 4.5 : : 4.5 : 13.5

**(3) Fill in the gaps:**

**Solution:-** (a) 11: 25 : : __22__ : 50

(b) 7: __56__ : : 8: 64

(c) 2.5 : 5.0 : : 7 : __14__

(d) 1/3 : 1/5 : : __7/6__ : 7/10

(e) __2.5__ : 12.5 : : 5 : 25

**(4) Determine the fourth proportional of the following quantities:**

**Solution:-** **(a) 5, 7, 10**

Let, the fourth proportion is x

Therefore, 5:7 : : 10: x

=> 5/7 = 10/x

=> x = 7/10/5

= 14

**(b) 15, 25, 33**

Let the 4^{th} proportion is x.

15: 25 : : 33 : x

=> 15/25 = 33/x

=> x = 25×33/15

= 55.

**(c) 16, 24, 32**

Let, the 4t proportion is x

16: 24 : : 32: x

=> 16/24 = 24×32/16

= 48

**(d) 8, 8 ½, 4**

= 8, 17/2, 4

Let, the fourth proportion is x

=> 8/17/2 = 7/x

=> x = 17×4/2×8

= 17/4.

**(e) 5, 4. 5, 7**

Let, the fourth proportion is x.

5: 4.5 : : 7: x

=> 5/4.5 = 7/x

=> x = 4.5×4/5

= 6.3.

**(5) If the price of 15 kg rice is TK. 600, what is the price of 25 kg rice?**

**Solution:- **Here, if the quantity of rice is rising then price also rise.

Let, price will be = x Rs

Therefore, Proportion will be,

15: 25 : : 600 : x

=> 15/25 = 600/x

=> x = 25×600/15

= 1000 Rs.

**(6) 550 shirts are made daily in a garments factory. How many shirts are made at the same rate rate in a week.**

**Solution:- **1 week = 7 days.

Daily 550 shirts are made,

Therefore, Proportion will be,

1: 7 : : 550 : x

=> 1/7 = 550/x

=> x = 7x 550

= 3850.

Therefore, 3850 shirts are made at the same rate in a week.

**(7) Ages of there sons of Mr. Kabir are 5 years and 9 years respectively. He gave TK. 4200 in the ratio of their ages. How much will each of them get?**

**Solution:- **Total Rs = 4200

Therefore, Ages of 3 son = 5: 7:9

Total = (5+7+9)

= 21.

1^{st} son get = 4200x 5/2

= 1000Rs.

2^{nd} son get = 4200x 7/21

= 1400Rs.

3^{rd} son get = 4200x 921

= 1800Rs.

**(8) If TK. 2160 is divided among Rumi, Jesmin and Kakali in the ratio of 1:2:3, how much will each of them get?**

**Solution:- **Total TK 2160/-

Ratio = 1: 2: 3

Total = (1+2+3) = 6

Therefore, Rumi get = (1/6x 2160) Rs

= 360 Rs

Jasmine get = (2/6x 2160) TK.

= 720TK.

Kakoli get = (2160x 3/6) TK.

= 1080 TK**.**

**(9) Some money are being divided among Labib, Sami and Saiam in the ratio of 5:4:2. If Siam gets TK. 180, determine how much will Labib and Sami get?**

**Solution:- **Given, Siyam get 180 TK.

Therefore, Ratio = 5: 4: 2

2 unit = 180 Rs

1 unit = 90Rs.

Therefore, Labib get = 5×90 = 450 Tk.

Sami get = 4×90 = 360 TK.

**(10) Sabuj, Dalim and Linkon are three brothers. Their father divided TK. 6300 amongst them. Thus Sabuj gets 3/5 parts of Dalim and Dalim gets double of Linkon. Find how much each of them will get.**

**Solution:- **Total = 6300 TK.

Sabuj : Dalim = 3/5 : 1

= 3:5

= 6:10

Dalim get, multiple of 20 linkon.

Therefore, Dalim linkon = 2:1

= 2×5 : 1:5

= 10: 5

Therefore, Total = (6+10+5) = 21.

Therefore, Sabuj get = (6/21x 6300) TK.

= 1800Tk.

Dalim get = ( 10/21 x 6300) TK.

= 3000 TK.

Linkon get = (5/21x 6300) TK

= 1500 TK.

**(11) A piece of ornament is made by mixing bronze, zinc and silver. In that piece of ornament, the ratio of bronze and zinc is 1:2 and the ratio of Zinc and Silver is 3:5. Find how many grams of silver there are in an ornament weighing 19 grams.**

**Solution:- **Bronze : Zinc = 1: = 3:6

Zinc : silver = 3:5 = 6: 10

Therefore, B: Z : S = 3: 6: 10

Total = (3+6+10) = 19

Therefore, Silver has = (19x 10/19) gm

= 10gm.

**(12) Two equal size glasses are filled with sweet drink. In that sweet drink, the ratio of water and syrup in the first glass is 3:2 in the second glass it is 5:4 respectively. If the sweet drink of two glasses are mixed together, find the ratio of water and surup.**

**Solution:- **1^{st} glass, water : syrup = 3:2

Total = 3+2 = 5

Therefore, water = 3/5 & syrup = 2/5

2^{nd} glass, water : syrup = 5:4

Total = (5+4) = 9

Therefore, water = 5/9; syrup = 4/9.

Therefore, total quantity of water

(3/5 + 5/9)

= 27+25/45

= 52/45

And syrup = (2/5 + 4/9)

= 18+20/45

= 38/45

Therefore, Ratio = 52/45 : 38/45

= 52:38

= 26:19

**(13) If a:b=4: 7, b:c= 10: 7, find a: b: c.**

**Solution:**

**(14) If TK. 9600 is divided amongst Sara, Mimuna and Raisa in the ratio of 4:3:1, how much taka will each of them get?**

**Solution:- **Total money = 9600TK.

Sara: mimuna: Raisa = 4: 3: 1

Total = (4+3+1) = 8.

Therefore, Sara get = (4/5x 9600) = 4800TK.

Mimuma get = (3/8×9600) = 3600 TK.

Raisa get = (1/8x 9600) = 1200 TK.

**(15) TK. 4200 is divided amongst three students in the ratio of their classes. If they are the students of class VI, VII, and VIII, how many taka will each of them get?**

**Solution:- **Total money = 4200TK.

Vi : VII: VIII = 6: 7: 8

Total = (6+7+8) = 21

Therefore class vi get = (4200x 6/2) TK.

= 1200TK.

Class vii get = (4200x 7/21)

= 1400TK.

Class viii get = (4200x 8/21) TK.

= 1600TK.

Thank you for your help 🤠