The price of 8080 apples is equal to that of 120120 oranges. The price of 6060 apples and 7575 oranges together is Rs. 1320. The total price of 2525 apples and 4040 oranges is ?
Answers
Step-by-step explanation:
Simplification #1
1. 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
A. Rs.
780
B. Rs.
660
C. Rs.
620
D. Rs.
820
Answer: Option C
Explanation:
Solution 1
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
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