the price of 80 apples is equal to that of 120 oranges. the price of 60 apples and 75 oranges together is rs 1320. the total price of 25 apples and 40 oranges is rs.?
find simplification
Answers
Answer:
Let price of one apple
=
a
price of one orange
=
b
Price of
80
apples = Price of
120
oranges
⇒
80
a
=
120
b
⇒
2
a
=
3
b
⇒
b
=
2
a
3
⋯
(
1
)
Price of
60
apples + Price of
75
oranges
=
Rs.
1320
⇒
60
a
+
75
b
=
1320
⇒
4
a
+
5
b
=
88
⇒
4
a
+
5
(
2
a
)
3
=
88
[∵ substituted value of
b
from
(
1
)
]
⇒
12
a
+
10
a
=
88
×
3
⇒
6
a
+
5
a
=
44
×
3
⇒
11
a
=
44
×
3
⇒
a
=
4
×
3
=
12
b
=
2
a
3
=
2
×
12
3
=
8
Total price of
25
apples and
40
oranges
=
25
a
+
40
b
=
25
×
12
+
40
×
8
=
300
+
320
=
620
Solution 2
80
apples
≡
120
oranges
⇒
2
apples
≡
3
oranges
⇒
60
apples
≡
90
oranges
60
apples
+
75
oranges
=
1320
⇒
90
oranges
+
75
oranges
=
1320
⇒
165
oranges
=
1320
⇒
1
orange
=
8
1
apple
=
3
×
8
2
=
12
25
apples
+
40
oranges
=
25
×
12
+
40
×
8
=
620
ANSWER ⤵️
Solution 1
Let price of one apple = a
Price of one orange = b
Price of 80 apples = Price of 120 oranges⇒
80a = 120b
⇒2a = 3b
⇒b = 2a / 3 -------- (1)
Price of 60 apples + Price of 75 oranges = Rs. 1320
⇒60a + 75b = 1320
⇒4a + 5b = 88
⇒4a + 5 (2a)3 = 88 [∵ substituted value of b from (1)]
⇒12a + 10a = 88 × 3
⇒6a + 5a = 44 × 3
⇒11a = 44 × 3
⇒a = 4 × 3 = 12
b = 2a/3 = 2 × 12/3 = 8
Total price of 25 apples and 40 oranges
= 25a + 40b
= 25 × 12 + 40 × 8
= 300 + 320 = 620
Solution 2
80 apples ≡ 120 oranges
⇒2 apples ≡ 3 oranges
⇒60 apples ≡ 90 oranges
60 apples + 75 oranges = 1320
⇒90 oranges + 75 oranges = 1320
⇒165 oranges = 1320
⇒1 orange = 8
1 apple = 3 × 8/2 = 12
25 apples + 40 oranges
= 25 × 12 + 40 × 8 = 620