Some Math Questions and Answers
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Question:
There were some boys and girls in a room.
If 24 boys leave the room, the total no. of students who remained in the room will be 7 times theno. of boys who remained the the room.
If 12 girls leave the room, the total no. of students who remained in the room will be 4 times the no. of boys.
How many students are there in the classroon?
Answer:
Boys at first = 1u + 24 = 1p ………… (1)
Girls at first = 6u = 3p + 12 ………… (2)
6u = 3(1u + 24) + 12
3u = 84
1u = 28
No. of students in classroom = 7u + 24 = 7(28 ) + 24 = 220
Reasoning:
If 24 boys leave the room:
At last
Boys : 1u
Girls : 6u
At first
Boys : 1u + 24
Girls : 6u
If 12 girls leave the room
At last
Boys : 1p
Girls : 3p
At first
Boys : 1p
Girls : 3p + 12
The number of boys and girls at first must be the same
1u + 24 = 1p ————– (1)
6u =3p + 12 ————— (2)
Solve to find the no. of boys and girls
Question:
1) 65% of the animals on a farm were cows and the rest were goats. When 240 more cows and goats were added to the farm, the percentage of cows increased by 20% and the number of goats doubled. How many goats were there on the farm at first?
Answer:
At first
Cows => 65% = 65u
Goats => 35% = 35u
At last
Cows => 65u + 13u = 78u
Goats => 35u + 35u = 70u
13u + 35u = 48u = 240
1u = 5
No. of goats at first = 35u = 35 x 5 = 175
Question:
2)There are some black and white marbles in a bag.If 20 black marbles are removed from the bag, the total number of marbles left will be 7 times the number of black marbles left. If 50 white marbles are removed from the bag, the total number of marbles left will be 5 times the number of black marbles left.How many marbles are there in the bag?
Answer:
If 20 black marbles removed
At lastBlack : 1u
White : 6u
At first
Black : 1u + 20
White : 6u
If 50 white marbles removed
At last
Black : 1p
White : 4p
At first
Black : 1p
White : 4p + 50
1u + 20 = 1p ————— (1)
6u = 4p + 50 —————-(2)
6u = 4( 1u + 20 ) + 50
6u = 4u + 130
2u = 130
1u = 65
No. of marbles in the bag = 7u + 20 = 7(65 ) + 20 = 475