CHUYÊN ĐỀ 4 - SỐ THẬP PHÂN, tỉ số %

["b\u00e1n m\u1ed9t s\u1ea3n ph\u1ea9m ch\u1ec9 t\u0103ng 10% th\u00ec ph\u1ea3i t\u0103ng th\u00eam s\u1ed1 l\u01b0\u1ee3ng s\u1ea3n ph\u1ea9m l\u00e0 bao nhi\u00eau \u0111\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c doanh thu \u0111\u00f3? H\u01b0\u1edbng D\u1eabn Gi\u1ea3i T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m c\u1ee7a doanh thu m\u1edbi v\u00e0 doanh thu c\u0169 l\u00e0: 100%+ 43% = 143% T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m c\u1ee7a gi\u00e1 s\u1ea3n ph\u1ea5m m\u1edbi v\u00e0 gi\u00e1 s\u1ea3n ph\u1ea9m c\u0169 l\u00e0: 100% + 10% = 110% T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m c\u1ee7a s\u1ed1 l\u01b0\u1ee3ng s\u1ea3n ph\u1ea9m sau khi t\u0103ng v\u00e0 tr\u01b0\u1edbc khi t\u0103ng l\u00e0: 143% : 110% = 130%. S\u1ed1 ph\u1ea7n tr\u0103m s\u1ed1 l\u01b0\u1ee3ng s\u1ea3n ph\u1ea5m c\u1ea7n t\u0103ng l\u00e0: 130% - 100% = 30%. \u0110\u00e1p S\u1ed1: 30% B\u00e0i 9: M\u1ed9t ng\u01b0\u1eddi mua hai c\u00e1i qu\u1ea1t \u0111i\u1ec7n, m\u1ed7i c\u00e1i gi\u00e1 1 000 000 \u0111\u1ed3ng. Ng\u01b0\u1eddi \u0111\u00f3 b\u00e1n c\u00e1i qu\u1ea1t \u0111\u1ea7u ti\u00ean b\u1ecb l\u1ed7 12% so v\u1edbi s\u1ed1 ti\u1ec1n mua c\u00e1i qu\u1ea1t \u0111\u00f3. Tuy v\u1eady, sau khi b\u00e1n hai c\u00e1i qu\u1ea1t, ng\u01b0\u1eddi \u0111\u00f3 v\u1eabn l\u00e3i 40 000 \u0111\u1ed3ng. V\u1eady ng\u01b0\u1eddi \u0111\u00f3 \u0111\u00e3 b\u00e1n c\u00e1i qu\u1ea1t th\u1ee9 hai \u0111\u01b0\u1ee3c l\u00e3i l\u00e0 ...% so v\u1edbi s\u1ed1 ti\u1ec1n mua c\u00e1i qu\u1ea1t \u0111\u00f3. H\u01b0\u00f3ng D\u1eabn Gi\u1ea3i S\u1ed1 ti\u1ec1n b\u1ecb l\u1ed7 khi b\u00e1n c\u00e1i qu\u1ea1t \u0111\u1ea7u ti\u00ean l\u00e0: 1 000 000 : 100 X 12 = 120 000 (\u0111\u1ed3ng) Do sau khi b\u00e1n hai c\u00e1i qu\u1ea1t v\u1eabn l\u00e3i 40 000 \u0111\u1ed3ng n\u00ean s\u1ed1 ti\u1ec1n l\u00e3i b\u00e1n c\u00e1i qu\u1ea1t th\u1ee9 hai v\u1eeba \u0111\u1ee7 b\u00f9 l\u1ed7 cho c\u00e1i qu\u1ea1t \u0111\u1ea7u ti\u00ean v\u00e0 c\u00f2n l\u00e3i th\u00eam 40 000 \u0111\u1ed3ng. S\u1ed1 ti\u1ec1n l\u00e3i khi b\u00e1n c\u00e1i qu\u1ea1t th\u1ee9 hai l\u00e0: 120 000 + 40 000 = 160 000 (\u0111\u1ed3ng) S\u1ed1 ph\u1ea7n tr\u0103m l\u00e3i khi b\u00e1n c\u00e1i qu\u1ea1t th\u1ee9 hai l\u00e0: 160 000 : 1 000 000 X 100% = 16% \u0110\u00e1p S\u1ed1: 16% B\u00e0i 10: Gi\u00e1 x\u0103ng th\u00e1ng ba so v\u1edbi th\u00e1ng hai t\u0103ng 15%. Gi\u00e1 x\u0103ng th\u00e1ng t\u01b0 so v\u1edbi gi\u00e1 x\u0103ng th\u00e1ng ba l\u1ea1i gi\u1ea3m \u0111i 15%. H\u1ecfi gi\u00e1 x\u0103ng th\u00e1ng t\u01b0 so v\u1edbi th\u00e1ng hai gi\u1ea3m \u0111i bao nhi\u00eau ph\u1ea7n tr\u0103m? H\u01b0\u1edbng D\u1ea9n Gi\u1ea3i T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m gi\u00e1 x\u0103ng th\u00e1ng 3 so v\u1edbi th\u00e1ng 2 l\u00e0: 100% + 15% = 115% T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m gi\u00e1 x\u0103ng th\u00e1ng 4 so v\u1edbi th\u00e1ng 3 l\u00e0:100% - 15% = 85% T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m gi\u00e1 x\u0103ng th\u00e1ng 4 so v\u1edbi th\u00e1ng 2 l\u00e0:85% X 115% = 97,75% Gi\u00e1 x\u0103ng th\u00e1ng 4 so v\u1edbi th\u00e1ng 2 gi\u1ea3m \u0111i s\u1ed1 ph\u1ea7n tr\u0103m l\u00e0:","100% - 97,75% = 2,25% \u0110\u00e1p S\u1ed1: 2,25% B\u00e0i 11: Gi\u00e1 c\u1ee7a m\u1ed9t chi\u1ebfc m\u0169 b\u1ea3o hi\u1ec3m l\u00e0 108 000 \u0111\u1ed3ng. \u0110\u1ec1 thu h\u00fat kh\u00e1ch h\u00e0ng, ng\u01b0\u1eddi ta quy\u1ebft \u0111\u1ecbnh h\u1ea1 gi\u00e1 17,5%. T\u00ednh gi\u00e1 b\u00e1n c\u1ee7a chi\u1ebfc m\u0169 b\u1ea3o hi\u1ec3m sau khi h\u1ea1 gi\u00e1. H\u01b0\u1edbng D\u1eabn Gi\u1ea3i S\u1ed1 ti\u1ec1n chi\u1ebfc m\u0169 \u0111\u01b0\u1ee3c gi\u1ea3m l\u00e0: 108000 X 17,5% = 18900 (\u0111\u1ed3ng) Gi\u00e1 b\u00e1n chi\u1ebfc m\u0169 b\u1ea3o hi\u1ec3m sau khi h\u1ea1 gi\u00e1 l\u00e0: 108000 - 18900 = 89100 (\u0111\u1ed3ng) \u0110\u00e1p s\u1ed1: 89 100 \u0111\u1ed3ng. B\u00e0i 12: M\u1ed9t c\u1eeda h\u00e0ng trong ng\u00e0y khai tr\u01b0\u01a1ng \u0111\u00e3 h\u1ea1 gi\u00e1 m\u1ed9t s\u1ea3n ph\u1ea5m 15% gi\u00e1 \u0111\u1ecbnh b\u00e1n l\u00fac \u0111\u1ea7u. Tuy v\u1eady, c\u1eeda h\u00e0ng v\u1eabn c\u00f2n l\u00e3i 19% so v\u1edbi ti\u1ec1n v\u1ed1n. H\u1ecfi n\u1ebfu c\u1eeda h\u00e0ng kh\u00f4ng h\u1ea1 gi\u00e1 th\u00ec c\u1eeda h\u00e0ng \u0111\u00f3 l\u00e3i \u0111\u01b0\u1ee3c bao nhi\u00eau ph\u1ea7n tr\u0103m so v\u1edbi ti\u1ec1n v\u1ed1n? H\u01b0\u00f3ng D\u1eabn Gi\u1ea3i T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m gi\u1eefa gi\u00e1 sau khi h\u1ea1 v\u00e0 gi\u00e1 \u0111\u1ecbnh b\u00e1n l\u00e0: 100% - 15% = 85% T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m gi\u1eefa gi\u00e1 sau khi h\u1ea1 v\u00e0 gi\u00e1 v\u1ed1n l\u00e0: 100% + 19% = 119% T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m gi\u1eefa gi\u00e1 b\u00e1n v\u00e0 gi\u00e1 v\u1ed1n l\u00e0: 119% : 85% = 140% N\u1ebfu kh\u00f4ng h\u1ea1 gi\u00e1 c\u1eeda h\u00e0ng \u0111\u00f3 l\u00e3i s\u1ed1 ph\u1ea7n tr\u0103m l\u00e0: 140% - 100% = 40% \u0110\u00e1p S\u1ed1: 40% B\u00e0i 13: T\u1ed5ng c\u1ee7a hai s\u1ed1 l\u00e0 25%, th\u01b0\u01a1ng c\u1ee7a hai s\u1ed1 c\u0169ng l\u00e0 25%. T\u00ecm hai s\u1ed1 \u0111\u00f3? H\u01b0\u00f3ng Dan Gi\u1ea3i \u0110\u1ed5i 25% = 1\/4 = 0,25. S\u1ed0 b\u00e9 l\u00e0: 0,25 : (1 + 4) X 1 =0,05 S\u1ed1 l\u1edbn l\u00e0: 0,25 - 0,05 = 0,2 \u0110\u00e1p S\u1ed1: 0,05 v\u00e0 0,2. B\u00e0i 14: \u0110\u1ea7u n\u0103m h\u1ecdc tr\u01b0\u1eddng em c\u00f3 s\u1ed1 h\u1ecdc sinh trai v\u00e0 g\u00e1i b\u1eb1ng nhau. Trong h\u1ecdc k\u1ef3 I tr\u01b0\u1eddng nh\u1eadn th\u00eam 15 em g\u00e1i v\u00e0 5 em trai. V\u00ec v\u1eady s\u1ed1 h\u1ecdc sinh g\u00e1i chi\u1ebfm 51% t\u1ed5ng s\u1ed1 h\u1ecdc sinh. H\u1ecfi \u0111\u1ea7u n\u0103m h\u1ecdc tr\u01b0\u1eddng em c\u00f3 bao nhi\u00eau h\u1ecdc sinh trai, bao nhi\u00eau h\u1ecdc sinh g\u00e1i? H\u01b0\u00f3ng D\u1ea9n Gi\u1ea3i Trong h\u1ecdc k\u1ef3 I s\u1ed1 h\u1ecdc sinh g\u00e1i h\u01a1n s\u1ed1 h\u1ecdc sinh trai l\u00e0: 1 5 - 5 = 10 h\u1ecdc sinh. S\u1ed1 h\u1ecdc sinh trai chi\u1ebfm: 100% - 5 1 % = 49% t\u1ed5ng s\u1ed1 h\u1ecdc sinh.","T\u1ec9 s\u1ed1 ph\u1ea7n tr\u0103m s\u1ed1 h\u1ecdc sinh g\u00e1i h\u01a1n h\u1ecdc sinh trai l\u00e0: 51 % - 49% = 2% t\u1ed5ng s\u1ed1 h\u1ecdc sinh. S\u1ed1 h\u1ecdc sinh c\u00e1 tr\u01b0\u1eddng trong h\u1ecdc k\u1ef3 I l\u00e0: 10 : 2% = 500 (h\u1ecdc sinh) S\u1ed1 h\u1ecdc sinh c\u1ea3 tr\u01b0\u1eddng \u0111\u1ea7u n\u0103m h\u1ecdc l\u00e0: 500 - (15 + 5) = 480 (h\u1ecdc sinh) S\u1ed1 h\u1ecdc sinh nam, n\u1eef c\u1ee7a tr\u01b0\u1eddng \u0111\u1ea7u n\u0103m h\u1ecdc l\u00e0: 480 : 2 = 240 (h\u1ecdc sinh) \u0110\u00e1p S\u1ed1: 240 h\u1ecdc sinh B\u00e0i 15: Trong m\u1ed9t ng\u00e0y h\u1ed9i to\u00e1n, \u0111\u1ed9i To\u00e1n c\u1ee7a m\u1ed9t kh\u1ed1i l\u1edbp chia th\u00e0nh ba nh\u00f3m. N\u1ebfu l\u1ea5y 40% s\u1ed1 h\u1ecdc sinh c\u1ee7a nh\u00f3m th\u1ee9 nh\u1ea5t chia \u0111\u1ec1u th\u00eam cho hai nh\u00f3m kia th\u00ec s\u1ed1 h\u1ecdc sinh c\u1ee7a ba nh\u00f3m s\u1ebd b\u1eb1ng nhau. Nh\u01b0ng n\u1ebfu nh\u00f3m th\u1ee9 nh\u1ea5t b\u1edbt \u0111i 3 h\u1ecdc sinh th\u00ec s\u1ed1 h\u1ecdc sinh c\u1ee7a nh\u00f3m th\u1ee9 nh\u1ea5t s\u1ebd b\u1eb1ng t\u1ed5ng s\u1ed1 h\u1ecdc sinh c\u1ee7a hai nh\u00f3m kia. H\u1ecfi s\u1ed1 h\u1ecdc sinh c\u1ee7a \u0111\u1ed9i To\u00e1n c\u1ee7a kh\u1ed1i l\u1edbp \u0111\u00f3? H\u01b0\u1edbng D\u1eabn Gi\u1ea3i M\u1ed7i nh\u00f3m nh\u1eadn th\u00eam 40% : 2 = 20% s\u1ed1 h\u1ecdc sinh nh\u00f3m th\u1ee9 nh\u1ea5t. Khi \u0111\u00f3 m\u1ed7i nh\u00f3m c\u00f3 s\u1ed1 h\u1ecdc sinh b\u1eb1ng: 100% - 40% = 60% s\u1ed1 h\u1ecdc sinh nh\u00f3m th\u1ee9 nh\u1ea5t. Ban \u0111\u1ea7u, m\u1ed7i nh\u00f3m th\u1ee9 hai v\u00e0 th\u1ee9 ba c\u00f3 s\u1ed1 h\u1ecdc sinh l\u00e0: 60% - 20% = 40% nh\u00f3m th\u1ee9 nh\u1ea5t. T\u1ed5ng s\u1ed1 h\u1ecdc sinh nh\u00f3m th\u1ee9 hai v\u00e0 th\u1ee9 ba l\u00e0: 40% + 40% = 80% s\u1ed1 h\u1ecdc sinh nh\u00f3m th\u1ee9 nh\u1ea5t. Nh\u01b0 v\u1eady khi b\u1edbt \u0111i 3 h\u1ecdc sinh nh\u00f3m th\u1ee9 nh\u1ea5t t\u1ee9c l\u00e0 b\u1edbt \u0111i: 100% - 80% = 20% s\u1ed1 h\u1ecdc sinh nh\u00f3m th\u1ee9 nh\u1ea5t. S\u1ed1 h\u1ecdc sinh nh\u00f3m th\u1ee9 nh\u1ea5t l\u00e0: 3 : 20% = 15 (h\u1ecdc sinh) S\u1ed1 h\u1ecdc sinh nh\u00f3m hai v\u00e0 ba l\u00e0: 15 - 3 = 12 (h\u1ecdc sinh) S\u1ed1 h\u1ecdc sinh c\u1ee7a \u0111\u1ed9i To\u00e1n c\u1ee7a kh\u1ed1i l\u1edbp l\u00e0: 15 + 12 = 27 (h\u1ecdc sinh) \u0110\u00e1p S\u1ed1: 27 h\u1ecdc sinh. B\u00e0i 16: Kh\u1ed1i l\u01b0\u1ee3ng c\u00f4ng vi\u1ec7c t\u0103ng 80%. H\u1ecfi phai t\u0103ng s\u1ed1 ng\u01b0\u1eddi lao \u0111\u1ed9ng th\u00eam bao nhi\u00eau ph\u1ea7n tr\u0103m \u0111\u1ec1 n\u0103ng su\u1ea5t lao \u0111\u1ed9ng t\u0103ng 20%? H\u01b0\u1edbng D\u1eabn Gi\u1ea3i Gi\u1ea3 s\u1eed kh\u1ed1i l\u01b0\u1ee3ng c\u00f4ng vi\u1ec7c ban \u0111\u1ea7u l\u00e0 100% v\u00e0 n\u0103ng su\u1ea5t lao \u0111\u1ed9ng l\u00fac \u0111\u1ea7u l\u00e0 100% th\u00ec khi \u0111\u00f3 kh\u1ed1i l\u01b0\u1ee3ng c\u00f4ng vi\u1ec7c m\u1edbi l\u00e0: 100% + 80% = 180% kh\u1ed1i l\u01b0\u1ee3ng c\u00f4ng vi\u1ec7c ban \u0111\u1ea7u. N\u0103ng su\u1ea5t lao \u0111\u1ed9ng m\u1edbi l\u00e0: 100% + 20% = 120% n\u0103ng su\u1ea5t lao \u0111\u1ed9ng ban \u0111\u1ea7u. S\u1ed1 ng\u01b0\u1eddi lao \u0111\u1ed9ng c\u1ea7n t\u0103ng th\u00eam l\u00e0: 180% : 120% X 100% = 150%. \u0110\u00e1p S\u1ed1: 150%."]