I . Shalvi wants to organize her birthday party. She was happy on her birthday. She is very health conscious, thus she decided to serve fruits only. She has 36 apples and 60 bananas at home and decided to serve them. She want to distribute fruits among guests. She does not want to discriminate among guests so she decided to distribute equally among all
1). How many maximum guests Shalvi can invite?
a) 12
b) 120
c) 6
d) 180
2). How many apples and bananas will each guest get?
a) 3 apple 5 banana
b) 2 apple 4 banana
c) 5 apple 3 banana
d) 4 apple 2 banana
3). Shalvi decide to add 42 mangoes also. In this case how many maximum guests Shalvi can invite
a) 12
b) 120
c)6
d) 180
4) . How many total fruits will each guest get now ?
a) 6 apple 5 banana and 6 mangoes
b) 6 apple 10 banana and 7 mangoes
c) 3 apple 5 banana and 7 mangoes
d) 3 apple 10 banana and 6 mangoes
5). If Shalvi decide to add 3 more mangoes and instead 6 apple, in this case how many maximum guests Shalvi can invite ?
a)12
b) 30
c) 15
d) 24
Answers
1)A
2)A
3)C
4)C
5)C
Hope it helps
Answer:
Shalvi has 36 apples and 60 bananas and she wants to distribute the fruits equally among all the guests.
To find:
The answers to the above questions.
Solution:
(i)
To find the maximum number of guests Shalvi can invite, we need to find the HCF of the quantities of two fruits which is the highest common factor between the two quantities.
Factors of 36 apples and 60 bananas are-
36 = 2 \times 2 \times 3 \times 336=2×2×3×3
60 = 2 \times 2 \times 3 \times 560=2×2×3×5
So, the highest common factor (HCF) between them is 2 × 2 × 3 = 12.
Hence, the maximum guests Shalvi can invite is (a) 12.
(ii)
As Shalvi wants to distribute the fruits equally among all the guests and the number of guests is 12. So,
The number of apples each guest will get =
\frac{total \: apples}{number \: of \: guests}
numberofguests
totalapples
\frac{36}{12} = 3
12
36
=3
Similarly, the number of bananas each guest will get =
\frac{total \: bananas}{number \: of \: guests} = \frac{60}{12} = 5
numberofguests
totalbananas
=
12
60
=5
Hence, each guest will get (a) 3 apples, 5 bananas.
(iii)
As Shalvi decides to add 42 mangoes, so we need to find out the HCF of quantities of all three fruits.
Factors of 36, 60 and 42 are-
36 = 2 \times 2 \times 3 \times 336=2×2×3×3
60 = 2 \times 2 \times 3 \times 560=2×2×3×5
42 = 2 \times 3 \times 742=2×3×7
So, the highest common factor (HCF) between them is 2 × 3 = 6.
Hence, after adding 42 mangoes, the maximum number of guests Shalvi can invite is (c) 6.
(iv)
As Shalvi wants to distribute the fruits equally among all the guests and the number of guests is 6. So,
The number of apples each guest will get =
\frac{total \: apples}{number \: of \: guests}
numberofguests
totalapples
\frac{36}{6} = 6
6
36
=6
Similarly, the number of bananas each guest will get =
\frac{total \: bananas}{number \: of \: guests} = \frac{60}{6} = 10
numberofguests
totalbananas
=
6
60
=10
Also, the number of mangoes each guest will get =
\frac{total \: mangoes}{number \: of \: guests} = \frac{42}{6} = 7
numberofguests
totalmangoes
=
6
42
=7
Hence, the total fruits each guest will get is (b) 6 apples, 10 bananas, 7 mangoes.
(v)
After adding 3 more mangoes instead of 6 apples so now,
The number of mangoes is = 45
The number of apples is = 36 - 6 = 30
The number of bananas is = 60
To find the maximum number of guests, so we need to find out the HCF of quantities of all three fruits.
Factors of 45, 30 and 60 are-
45 = 3 \times 3 \times 5 \times 345=3×3×5×3
60 = 2 \times 2 \times 3 \times 560=2×2×3×5
30 = 2 \times 3 \times 530=2×3×5
So, the highest common factor (HCF) between them is 3 × 5 = 15.
Hence, after adding 3 mangoes at the place of 6 apples, the maximum number of guests Shalvi can invite is (c) 15.
