Question

Please solve all questions:-​

Answer 1

QUESTION 1 :-

TO FIND :- a : b : c

GIVEN :-

a : b = 5 : 8

b : c = 6 : 7

$\dfrac{a}{b} = \dfrac{5}{8}$

Expressing 'a' in terms of b,

$a = \dfrac{5b}{8}$

$\dfrac{b}{c} = \dfrac{6}{7}$

Expressing 'c' in terms of b,

$c = \dfrac{7b}{6}$

Hence a:b:c =

$\dfrac{5b}{8} : b : \dfrac{7b}{6}$

Since we are comparing, by taking the LCM,

LCM = 24

$\dfrac{15}{24} : \dfrac{24b}{24} : \dfrac{28b}{24}$

RATIO :- 15 : 24 : 28

QUESTION 2 :-

TO FIND :- THE AMOUNT RECEIVED BY EACH

GIVEN :- Total amount to be shared =≥ ₹5400 in the ratio 2:3:4 between Ram, Gita and Anu

Let the shares be 2x,3x and 4x

2x + 3x + 4x = 5400

9x = 5400

$x = \dfrac{5400}{9}$

$x = 600$

Hence there shares are :

₹1200(2×600), ₹1800(3×600) and ₹24 00(4×600)

QUESTION 3 :-

TO FIND :- THE NUMBER OF COINS OF EACH TYPE

GIVEN :- A bag contains 50 paise, 20paise and 10paise at the ratio of 4:8:6. Total amount in the bag is ₹210

Value of 4x number of coins in 50paise = 50×4x = 200x

Value of 8x number of coins in 20paise = 20×8x = 160x

Value of 6x number of coins in 10paise = 10×6x = 60x

Hence, total = ₹210

₹1 = 100paise

₹210 = 21000paisw

by forming the equation,

200x + 160x + 60x = 21000

420x = 21000

$x = \dfrac{21000}{42}$

$x = 50$

Therefore the number of :

50paise coins = 200 (4×50)

20paise coins = 400 (8×50)

10paise coins = 300 (6×50)

QUESTION 4 :-

GIVEN :-

15 litres mixture has water and milk in the ratio 2:4

The milk quantity is decreased by 3 litres/ water quantity increases by 3 litres.

TO FIND :- RATIO OF THE MIXTURE NOW.

Let the quantities be 2x and 4x respectively.

2x + 4x = 15

6x = 15

$x = \dfrac{15}{6}$

$x = \dfrac{5 }{2}$

Therefore quantity of each liquid :

$water \: = 2( \dfrac{5}{2}) = 2$

$milk \: = 4( \dfrac{5}{2}) = 10$

According to the question,

3 litres is increased in quantity of water.

New quantity of water = 2+3 = 5 litres

New quantity of milk = 10-3 = 7litres.

Hence new ratio = 5:7

Answer 2

Answer:

QUESTION 1 :-

TO FIND :- a : b : c

GIVEN :-

a : b = 5 : 8

b : c = 6 : 7

\dfrac{a}{b} = \dfrac{5}{8}

b

a

=

8

5

Expressing 'a' in terms of b,

a = \dfrac{5b}{8}a=

8

5b

\dfrac{b}{c} = \dfrac{6}{7}

c

b

=

7

6

Expressing 'c' in terms of b,

c = \dfrac{7b}{6}c=

6

7b

Hence a:b:c =

\dfrac{5b}{8} : b : \dfrac{7b}{6}

8

5b

:b:

6

7b

Since we are comparing, by taking the LCM,

LCM = 24

\dfrac{15}{24} : \dfrac{24b}{24} : \dfrac{28b}{24}

24

15

:

24

24b

:

24

28b

RATIO :- 15 : 24 : 28

QUESTION 2 :-

TO FIND :- THE AMOUNT RECEIVED BY EACH

GIVEN :- Total amount to be shared =≥ ₹5400 in the ratio 2:3:4 between Ram, Gita and Anu

Let the shares be 2x,3x and 4x

2x + 3x + 4x = 5400

9x = 5400

x = \dfrac{5400}{9}x=

9

5400

x = 600x=600

Hence there shares are :

₹1200(2×600), ₹1800(3×600) and ₹24 00(4×600)

QUESTION 3 :-

TO FIND :- THE NUMBER OF COINS OF EACH TYPE

GIVEN :- A bag contains 50 paise, 20paise and 10paise at the ratio of 4:8:6. Total amount in the bag is ₹210

Value of 4x number of coins in 50paise = 50×4x = 200x

Value of 8x number of coins in 20paise = 20×8x = 160x

Value of 6x number of coins in 10paise = 10×6x = 60x

Hence, total = ₹210

₹1 = 100paise

₹210 = 21000paisw

by forming the equation,

200x + 160x + 60x = 21000

420x = 21000

x = \dfrac{21000}{42}x=

42

21000

x = 50x=50

Therefore the number of :

50paise coins = 200 (4×50)

20paise coins = 400 (8×50)

10paise coins = 300 (6×50)

QUESTION 4 :-

GIVEN :-

15 litres mixture has water and milk in the ratio 2:4

The milk quantity is decreased by 3 litres/ water quantity increases by 3 litres.

TO FIND :- RATIO OF THE MIXTURE NOW.

Let the quantities be 2x and 4x respectively.

2x + 4x = 15

6x = 15

x = \dfrac{15}{6}x=

6

15

x = \dfrac{5 }{2}x=

2

5

Therefore quantity of each liquid :

water \: = 2( \dfrac{5}{2}) = 2water=2(

2

5

)=2

milk \: = 4( \dfrac{5}{2}) = 10milk=4(

2

5

)=10

According to the question,

3 litres is increased in quantity of water.

New quantity of water = 2+3 = 5 litres

New quantity of milk = 10-3 = 7litres.

Hence new ratio = 5:7