26 May Basic Maths
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Maths Maths Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
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What is 2+3-1*5/3(21*2)? • • • • • •
BODMAS rule. Step 1: solve bracket – which gives 0 Step 2: solve 5/3 – which gives 1.67 Multiply 1*1.67*0 = the result is 0 Add 2 and 3 and 0, Answer is 5. www.afterschoool.tk
What is average of first 18 multiples of 6? step: 1. the numbers are 6,12,18,24 and so on. This is AP (because in AP each number increases at constant difference. We can take 6 as common out of these – now series is : 6{1,2,3,4, … till 18}. For additing a series , we use formula n/2(first term+last term) = 18/2(1+18) 171 multiply it by 6 = 1026 (it is total of 18 numbers) Step 2: average = total / no. = 1026/18 =57 Ans.
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Average of 11 results is 50, if average of first 6 results is 49 and that of last 6 is 52, which is 6th no.? • Step 1: total of 11 = 11*50 = 550. (total is equal to no. of items * average value of each). • Step 2: total of first 6: 6*49 =294. • Step 3: total of last 6: 6*52 =312 • Add these : 294+312 = 606 • Since sixth item has been counted twice (in first and last six both), so sixth item is 606 -550 • = 56 Ans.
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Find the average of first 12 prime numbers? • First 12 prime numbers are: 2,3,5,7,11,13,17,19,23,29,31,37 • Now add these : 197 • Now divide 197 by 12 • =16.4 approx. Ans.
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If there are five consecutive odd digits – a,b,c,d,e. what is the average of these?
• Average is C. ans.
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Average age of a family (husband and wife) was 23 years, when they were married 5 years back. The average age of this family (with one child) is now 20 years. How old is the child?
• Step 1: total of family (of 2) age: 23*2 =46 (5 years back) so add 10 to get present age : 56. • Step 2: total of family of 3: 3*20 = 60. • Age of child: 60-56 • =4 ans. www.afterschoool.tk
Average of 6 numbers is 30, if the average of first four is 25 and last three is 35, what is the forth number?
Total of 6 no. = 6*30 = 180 Total of first 4= 4*25 =100 Total of last 3: 3*35= 105 Total of first four and last 3= 205 Forth number has been counted twice. So forth no is 205-180 • ==25 Ans. • • • • •
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Average age of 3 boys is 16 and their age are in the ratio of 4,5,7 – what are their ages?
• Total of their age: 3*16 = 48 • Age of firs is 4/(4+5+7) =4/16*48 =12. • Similarly age of second is 15 and III is 21 • So ans: 12,15,21. ans.
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What is the mean proportional beteween 7 & 28? • Formulae for calculating mean proportion is : (a*b)^1/2 • So square root of (7*28) = 14Ans.
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What is third proportional to 9,12? • First multiplied to third is equal to square of second number. • Let us assume the third proportion is X. by formulae, 9X = 12*12. • = 16 Ans.
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The ratio of number of boys and girls in a school of 720 students is 7:5, how many girls should be admitted to make ratio 5:7? • No. of boys: 720 *(7/(7+5)) =420 • No. of girls: 720 *(5/(7+5)) =300. • Now in order to make ratio to 5:7. we have to get desired no. of girls. No. of boys will remain same, so taking it as base: 420*(7/5) =588 • No. of girls required: 588-300 =288 Ans.
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The ratio of number of boys and girls in a school of 720 students is 7:5, some boys quit and ratio becomes 5:7. How many boys quit the school? • No. of boys: 720 *(7/(7+5)) =420 • No. of girls: 720 *(5/(7+5)) =300. • Now in order to make ratio to 5:7. we have to get desired no. of boys. No. of girls will remain same, so taking it as base: 300*(5/7) = 215 • No. of boys quitting: 420-215 = 205 Ans.
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www.afterschoool.tk
What is mean proportional to 9,12? • It is equal to square root of 9*12 • It is equal to 2*3*3^1/2 • = 10.2 approx. Ans.
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www.afterschoool.tk
What is arithmetic mean of 9,12? • Add 9 and 12 = 21. • Divide 21 / 2 = 10.5 ans.
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www.afterschoool.tk
What is geometric mean of 9,16? • Find square root of 9*16 = 12 ans.
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What is harmonic mean to 9,12? • • • • •
Reverse 9 and 12 and add them, 1/9 +1/12 = 21/108 (a+b/ab). Multiply 21/108 by ½ = 21/216 Reverse 21/216, you get: 216/21 Ans. = 10.28 approx. ans.
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A mixture contains milk and water in the ratio of 5:1, on adding 5 liters of water, the ratio of milk and water becomes 5:2. the quantity of milk in the original mixture was? What is the quanitity of milk now?
• Here milk is 5, water is 2 (earlier 1). • The ratio has incresed from 5:1 to 5:2, it means water has incerased by 1. 1 is equal to 5 liters, so milk which is 5 is equal to 5*5 =25 Ans. Milk is still the same. www.afterschoool.tk
Some money was divided between Ram and Shyam in the ratio of 4:3, shyam gets 4800, what is total amount?
• • • •
If total amount is 7, shyam gets 3, If shyam gets 3, total amount is 7, By same logic total amount is : 7/3 *4800 = 11200 ans.
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Material labour and overhead cost are in ratio of 5:3:1, plus, you have to add margin of 20% and get selling price, and then you have to offer 10% discount, if material cost is 690, what is the final sale price (after discount) of an item?
• Total cost : 5+3+1 = 9, so it should be: 9/5*690 = 1242. add 20% margin: • 1242*1.2 = 1490.4 • Now give discount : 1490.4*.9 = 1341.36 Ans. www.afterschoool.tk
Rs 770 have been divided among ABC such that A gets 2/9 B *C together. , B gets 4/7 of A & C together. what is the shares of ABC respectively?
• If A gets 2, B+C get 9. that means A gets 2/ (2+9) *770 = 140 • If B gets 4, A &C get 7, so B gets 4/ (4+7) *770 = 280 • Remaining belong to C = 770 – (140+280) = 770-420 = 350 Ans.
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Rs. 510 have been divided among ABC such that A gets 2/3 of B, B gets ¼ of C. what is the shares of ABC respectively?
• Denominators of 2/3 and ¼ are 3 &4 respectively. • Take LCM of 3&4: 12. • Start from last, Let us assume that C gets 12, B gets 3, A gets 2. their ratio is 2:3:12. A gets: 2/(2+3+12) * 510 =60, B= 90, C = 360 ans.
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
www.afterschoool.tk
What is 2+3-1*5/3(21*2)? • • • • • •
BODMAS rule. Step 1: solve bracket – which gives 0 Step 2: solve 5/3 – which gives 1.67 Multiply 1*1.67*0 = the result is 0 Add 2 and 3 and 0, Answer is 5. www.afterschoool.tk
What is average of first 18 multiples of 6? step: 1. the numbers are 6,12,18,24 and so on. This is AP (because in AP each number increases at constant difference. We can take 6 as common out of these – now series is : 6{1,2,3,4, … till 18}. For additing a series , we use formula n/2(first term+last term) = 18/2(1+18) 171 multiply it by 6 = 1026 (it is total of 18 numbers) Step 2: average = total / no. = 1026/18 =57 Ans.
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Average of 11 results is 50, if average of first 6 results is 49 and that of last 6 is 52, which is 6th no.? • Step 1: total of 11 = 11*50 = 550. (total is equal to no. of items * average value of each). • Step 2: total of first 6: 6*49 =294. • Step 3: total of last 6: 6*52 =312 • Add these : 294+312 = 606 • Since sixth item has been counted twice (in first and last six both), so sixth item is 606 -550 • = 56 Ans.
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Find the average of first 12 prime numbers? • First 12 prime numbers are: 2,3,5,7,11,13,17,19,23,29,31,37 • Now add these : 197 • Now divide 197 by 12 • =16.4 approx. Ans.
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If there are five consecutive odd digits – a,b,c,d,e. what is the average of these?
• Average is C. ans.
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Average age of a family (husband and wife) was 23 years, when they were married 5 years back. The average age of this family (with one child) is now 20 years. How old is the child?
• Step 1: total of family (of 2) age: 23*2 =46 (5 years back) so add 10 to get present age : 56. • Step 2: total of family of 3: 3*20 = 60. • Age of child: 60-56 • =4 ans. www.afterschoool.tk
Average of 6 numbers is 30, if the average of first four is 25 and last three is 35, what is the forth number?
Total of 6 no. = 6*30 = 180 Total of first 4= 4*25 =100 Total of last 3: 3*35= 105 Total of first four and last 3= 205 Forth number has been counted twice. So forth no is 205-180 • ==25 Ans. • • • • •
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Average age of 3 boys is 16 and their age are in the ratio of 4,5,7 – what are their ages?
• Total of their age: 3*16 = 48 • Age of firs is 4/(4+5+7) =4/16*48 =12. • Similarly age of second is 15 and III is 21 • So ans: 12,15,21. ans.
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What is the mean proportional beteween 7 & 28? • Formulae for calculating mean proportion is : (a*b)^1/2 • So square root of (7*28) = 14Ans.
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What is third proportional to 9,12? • First multiplied to third is equal to square of second number. • Let us assume the third proportion is X. by formulae, 9X = 12*12. • = 16 Ans.
www.afterschoool.tk
The ratio of number of boys and girls in a school of 720 students is 7:5, how many girls should be admitted to make ratio 5:7? • No. of boys: 720 *(7/(7+5)) =420 • No. of girls: 720 *(5/(7+5)) =300. • Now in order to make ratio to 5:7. we have to get desired no. of girls. No. of boys will remain same, so taking it as base: 420*(7/5) =588 • No. of girls required: 588-300 =288 Ans.
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The ratio of number of boys and girls in a school of 720 students is 7:5, some boys quit and ratio becomes 5:7. How many boys quit the school? • No. of boys: 720 *(7/(7+5)) =420 • No. of girls: 720 *(5/(7+5)) =300. • Now in order to make ratio to 5:7. we have to get desired no. of boys. No. of girls will remain same, so taking it as base: 300*(5/7) = 215 • No. of boys quitting: 420-215 = 205 Ans.
www.afterschoool.tk
www.afterschoool.tk
What is mean proportional to 9,12? • It is equal to square root of 9*12 • It is equal to 2*3*3^1/2 • = 10.2 approx. Ans.
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www.afterschoool.tk
What is arithmetic mean of 9,12? • Add 9 and 12 = 21. • Divide 21 / 2 = 10.5 ans.
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www.afterschoool.tk
What is geometric mean of 9,16? • Find square root of 9*16 = 12 ans.
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What is harmonic mean to 9,12? • • • • •
Reverse 9 and 12 and add them, 1/9 +1/12 = 21/108 (a+b/ab). Multiply 21/108 by ½ = 21/216 Reverse 21/216, you get: 216/21 Ans. = 10.28 approx. ans.
www.afterschoool.tk
A mixture contains milk and water in the ratio of 5:1, on adding 5 liters of water, the ratio of milk and water becomes 5:2. the quantity of milk in the original mixture was? What is the quanitity of milk now?
• Here milk is 5, water is 2 (earlier 1). • The ratio has incresed from 5:1 to 5:2, it means water has incerased by 1. 1 is equal to 5 liters, so milk which is 5 is equal to 5*5 =25 Ans. Milk is still the same. www.afterschoool.tk
Some money was divided between Ram and Shyam in the ratio of 4:3, shyam gets 4800, what is total amount?
• • • •
If total amount is 7, shyam gets 3, If shyam gets 3, total amount is 7, By same logic total amount is : 7/3 *4800 = 11200 ans.
www.afterschoool.tk
Material labour and overhead cost are in ratio of 5:3:1, plus, you have to add margin of 20% and get selling price, and then you have to offer 10% discount, if material cost is 690, what is the final sale price (after discount) of an item?
• Total cost : 5+3+1 = 9, so it should be: 9/5*690 = 1242. add 20% margin: • 1242*1.2 = 1490.4 • Now give discount : 1490.4*.9 = 1341.36 Ans. www.afterschoool.tk
Rs 770 have been divided among ABC such that A gets 2/9 B *C together. , B gets 4/7 of A & C together. what is the shares of ABC respectively?
• If A gets 2, B+C get 9. that means A gets 2/ (2+9) *770 = 140 • If B gets 4, A &C get 7, so B gets 4/ (4+7) *770 = 280 • Remaining belong to C = 770 – (140+280) = 770-420 = 350 Ans.
www.afterschoool.tk
Rs. 510 have been divided among ABC such that A gets 2/3 of B, B gets ¼ of C. what is the shares of ABC respectively?
• Denominators of 2/3 and ¼ are 3 &4 respectively. • Take LCM of 3&4: 12. • Start from last, Let us assume that C gets 12, B gets 3, A gets 2. their ratio is 2:3:12. A gets: 2/(2+3+12) * 510 =60, B= 90, C = 360 ans.
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
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