Ajay went to a market and purchased a
distinct number of oranges, bananas and
apples. He bought a total of 80 fruits and at
least 24 fruits of each variety. The cost of
each orange, each apple and each banana is
Rs. 7, Rs. 3 and Rs. 5 respectively. If instead,
the cost of each orange, each apple and each
banana were Rs. 8, Rs. 3 and Rs. 9
respectively; his expenditure would have
been Rs. 140 more. The number of oranges
that Ajay purchased is:
Answers
Solution :-
Let us assume that, Ajay purchased O number of oranges , B number of bananas and A number of apples . { where O,B,A ≥ 24)
so,
→ O + B + A = 80 (total) ---------- Eqn.(1)
also,
→ (8O + 3A + 9B) - (7O + 3A + 5B) = 140 --------- Eqn.(2)
→ O + 4B = 140
conclusion :-
- O must be divisible by 4 .
- O = 24, 28 or 32 .
- If O = 24 => B = 29
- if O = 28 => B = 28 .
- If O = 32 => B = 27 .
checking all three possible cases now,
(1) If O =24 , B = 29 :-
→ 24 + 29 + A = 80
→ A = 80 - 53 = 27 .
then, putting all three values in Eqn.(2) ,
→ (8*24 + 3*27 + 9*29) - (7*24 + 3*27 + 5*29) = 140
→ (192 + 81 + 261) - (168 + 81 + 145) = 140
→ 534 - 394 = 140
→ 140 = 140 .
(2) If O =28 , B = 28 :-
→ 28 + 28 + A = 80
→ A = 80 - 56 = 24 .
then, putting all three values in Eqn.(2) ,
→ (8*28 + 3*24 + 9*28) - (7*28 + 3*24 + 5*28) = 140
→ (224 + 72 + 252) - (196 + 72 + 140) = 140
→ 548 - 408 = 140
→ 140 = 140 .
(3) If O = 32 , B = 27 :-
→ 32 + 27 + A = 80
→ A = 80 - 53 = 21
since A ≥ 24 . Case (3) is not Possible.
therefore, we can conclude that, The number of oranges that Ajay purchased are 24 or 28 .
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