Question
Four years back in time, a father was 3 times as old as his son then was. 8 years later father will be 2 times as old as his son will then be. Find the ages of son and father.
Hint:
let present ages of son is x years and present age of father is y years
Find both the ages 4 years back and apply the condition.
Find both ages after 8 yrs and apply the condition.
Solve the two equation to get the age of son and father.
The correct answer is: 40 years .
Ans :- Age of Son is 16 years and Age of father is 40 years .
Explanation :-
Step 1:- frame the equations from the given set of conditions .
let present ages of son is x years and present age of father is y years
Fours years back, age of son = x-4
Fours years back, age of father = y-4
Four years back in time, a father was 3 times as old as his son then was
![left parenthesis y minus 4 right parenthesis equals 3 space cross times space left parenthesis x minus 4 right parenthesis](data:image/png;base64,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)
—Eq1
After 8 years, age of son = x+8
After 8 years, age of father = y+8
8 years later father will be 2 times as old as his son will then be
![not stretchy rightwards double arrow left parenthesis y plus 8 right parenthesis equals 2 left parenthesis x plus 8 right parenthesis not stretchy rightwards double arrow y plus 8 equals 2 x plus 16](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARAAAAARCAYAAAAVIfMEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAA99JREFUeNrtW2FklVEYPq6ZZCIzM/0Yk8nkGpPMJGOS5EpkJknGZCb96F/Sj4wr2Y/pT7IfSSKZTBKTzDWJyUyS6EeS/s/MdY31nvZMp8/57j332znv99677+Hhfts59zvfc57vPe97vu8qFRaTxKKShyLGJgFSNZKoVYZ9hDzxg+DxLWOMmUaNoVWGfQZtuv6Uzn2QOEvcIJaJb4lHIm0GiKUA5x4iviSuEyvEVeJlgRpJ0EryNXN7IQ30Eu9gXNVwgvgC16H1WiCeDjmwftwcaWGOOE1sIbYiDf9oaVfCzeETS8QxYhuO+6DFmDCNJGgl/Zq5vJAWnhIniNtV2kwgYPTi+BCCYNAF5T5xyvN3btfRthw5zmEFiOIG0/5DN3GNQaNm0ErSNXN5IQ0NXPrpgLfic4C3EIFqQaeEpyxRf9TS9iZWA5/ibBhRf9cgPy3tBonvmIxTdtBIYzzmRr2H/6kG08rVMxL9weWFNObdpd8j39nSbeIP1HbVsI7U0MRVrLrRWvQbsd2zOLNYMU3zP7C0a8VY485Xi64YtJQrNo128YnYaRxfIz4MtBL50MqHZyT6g8sLacy7S7+vxK4kX+bCaURuG7YsfzuHjRgTd7GJ41ucPFLSCurQ3zGrvWJIXQ+gvh5y0GgXZ4kz+DySYOXn1sqHZ6T6g8MLacy7S78y9j7miZvQa0V52Aiew0mf1RFA9Cry2TjuIH6HqD6jfjfG1WWs8AM4V545gBwmviKecdTIxKLa2eledViBG0GrWp6R6g8OL3DPu2sA2UZWpIN7C4L/ELLCyb1mIMUqq0lcer5pfJ5Bfes7us7HGGGY+J6xhOmBYY7WqZFZ+1cSmlqiVrU8I9EfXF7gnnfXfnq+bY+39RPEXyH3QBZj2pQgZg8ifi6AOOU6/hdqE/UY8TFq+Ho1Uurf+wMzCTexJGnl6hmJ/uDyAve8u/Z7U2UOEmWjeke9zaFd3CPKJ8QCUsgrgcT5EhPp+1DrmpiybNztFZ2o5VsSaqRvngUYrg01Z3sDa+XqGYn+4PIC97y79tNlymhMUAzx3sx/Kc5yTHqma+E1jxcZxUWYZBjRM4fPekW7blnxfL8c9RoCJ9GoA1HfNM55tfPCTzNqJd0fXF7gnnfXfrps1ZvM40YQPIn5GQnshb+/8YjWcRcw2ELgc1/C5k8FaekSzm0i1OvZ9dTJpkatqM9tNedztbND32xaKcH+4PJCWvOuHD3agRJMvzuzBa04nlhZfyhWUHJ+PJb9mE6eVoUG0SMDE3RKWIxsygwKGJeu5SeEaiQNnFpJ8UcGgTiOmjBDhswfTYI/4XPZbkUfpEgAAAFMdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjFEMjs8L21vPjxtbz4oPC9tbz48bWk+eTwvbWk+PG1vPis8L21vPjxtbj44PC9tbj48bW8+KTwvbW8+PG1vPj08L21vPjxtbj4yPC9tbj48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4rPC9tbz48bW4+ODwvbW4+PG1vPik8L21vPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxRDI7PC9tbz48bWk+eTwvbWk+PG1vPis8L21vPjxtbj44PC9tbj48bW8+PTwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE2PC9tbj48L21hdGg+Nph8qAAAAABJRU5ErkJggg==)
— Eq2
Step 2:- find x by eliminating y
Doing Eq1-Eq2 to eliminate x
![left parenthesis 3 x minus 8 right parenthesis minus left parenthesis 2 x plus 8 right parenthesis equals y minus y not stretchy rightwards double arrow x minus 16 equals 0](data:image/png;base64,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)
∴ x= 16
Step 3:- substitute x=16 in Eq2.
![y equals 2 left parenthesis 16 right parenthesis plus 8 not stretchy rightwards double arrow y equals 32 plus 8](data:image/png;base64,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)
∴ y = 40
∴ The present age of son =x=16 years and present age of father = 40 years
Related Questions to study
A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.
A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.
The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where
.
![M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50](data:image/png;base64,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)
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?
Note:
We could have also used the first derivative test to find the local
maxima. We need to find critical points and then check whether the
function is increasing or decreasing on either side of the critical
point. If the function is increasing , i. e ., on the left side
and the function is decreasing, i. e ., on the right hand side, then we say that is a local maxima.
The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where
.
![M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50](data:image/png;base64,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)
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?
Note:
We could have also used the first derivative test to find the local
maxima. We need to find critical points and then check whether the
function is increasing or decreasing on either side of the critical
point. If the function is increasing , i. e ., on the left side
and the function is decreasing, i. e ., on the right hand side, then we say that is a local maxima.
Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z
Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z
Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.
Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.
Find the area of the polygon in the given picture,
cm, ![MB equals 4 cm text and end text MA equals 2 cm](data:image/png;base64,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)
![](data:image/png;base64,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)
Find the area of the polygon in the given picture,
cm, ![MB equals 4 cm text and end text MA equals 2 cm](data:image/png;base64,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)
![](data:image/png;base64,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)
A man bought 3 paise and 5 paise denomination stamps for Rs 1.00. In total he bought 22 stamps. Find out total number of 3 paise stamps bought by him.
A man bought 3 paise and 5 paise denomination stamps for Rs 1.00. In total he bought 22 stamps. Find out total number of 3 paise stamps bought by him.
A ball pen costs Rs 3.50 more than pencil. Adding 3 ball pens and 2 pencils sum up to Rs 13. Taking y and z as costs of ball pen and pencil respectively. Write down 2 simultaneous equations in terms of y and z which satisfy the above statement. Find out the values of y and z.
A ball pen costs Rs 3.50 more than pencil. Adding 3 ball pens and 2 pencils sum up to Rs 13. Taking y and z as costs of ball pen and pencil respectively. Write down 2 simultaneous equations in terms of y and z which satisfy the above statement. Find out the values of y and z.
In a town there are 2 brothers namely Anand and Suresh. Adding 1/3 rd anand’s age and suresh age would sum up to 10. Also adding Anand’s age together with 1⁄2 of suresh age would sum up to 10. Find Anand and Suresh ages.
In a town there are 2 brothers namely Anand and Suresh. Adding 1/3 rd anand’s age and suresh age would sum up to 10. Also adding Anand’s age together with 1⁄2 of suresh age would sum up to 10. Find Anand and Suresh ages.
From a cylindrical wooden log of length 30 cm and base radius 72 cm, biggest cuboid of square base is made. Find the volume of wood wasted?
From a cylindrical wooden log of length 30 cm and base radius 72 cm, biggest cuboid of square base is made. Find the volume of wood wasted?
Find the area of the figure.![GE equals 14 cm comma HF equals 10 cm comma AD equals 24 cm straight & BC equals 12](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUMAAAAPCAYAAAB+3q2kAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAABNNJREFUeNrtW29EXWEYf13JlSuSJJlLkmTmkn3I/RQzk7kSM5kkkczM9GVmMtmXmUz2IZJMMpHMTB9iMtfsw8jMJBOZ7EMSfZjkui53z5PfdU/nvvec99zOn/fezsOjztt73vOe3/s8v+d5n/MmxEXpJV0n/UeaIT0iXSbtE6WSt1C3pYt0mvSnYv+7Hs2jEsk7/JtfmKri2kg6T/oduoA2neSZwhoUNAf7fkfa6dF8kgY/ygLfB5rbbTvplmG+CRss/5L+Jv2Ae80SJ50l3cWYe6QvSZsDsmVHazKGid8hjaAtSjpMmnbo5G7LCumE4jNjeI9qJkOdcGUHSZkcdksjIkxg/t0OcGaHHIWDTnkwpzT8JobrHtJvaNPVbnl+/fj9NohOBcthBEmjsL1sm7ikjXScdDMgW1ZeEzakfdIml5w8CGIpyAJAD8nw8nO8R/pW0j5n49h+CjvBEtTp+7WSHsJpvRbOlH5pbLdZA3HxzzNFLCO4VxhIximX+M0RlmsyD1b16qF+vWjSkLXkLfqkUQY4IB2RjD+AyJZBal2IJv2IghlEla4aJ8N1ZAlm6cffgsSV5Zohg9nFtdM1mJS8i1eS0dhuv+B+ge3jvCKWjPkPE6k/1DT5UFqT/TL7frcemlfQyz6zHiwft+jLW6pj0kFENDaK96bxJ2AYPWgbRXY0YGofgeEFSYZe43oCXGVYHwWMq0BNquB4/PN1BWvQhjqSl/iy9IGIdLXbW6R/QLh8X50NlhEESu7fa/j7QQVc4hdHKK1J1sXJB8X6r0gf2fTlaPnYZvx1w3bBGD0WJO05FxZZpX9Q0TRns60KEtcYgniBrOvgzLEKHCTrMb5RZGZJTe12FOUCJtwxB/bMAfG6z1i6RYZl1yTr4UP9eNEbEoaX9eUMoNFm/KjD9lreJucUtxdB4MpfkKdNbXz91OF4VvUxN4RrZx/LlBt0sFuuC29inlOi9ANHpsy99cgmN/Ae1USGVmtynto2VPF2jhm+04U5511qr5Vt8lGZbXLUtE32G9c6IS/S8/WeJBOyGo/tZscjfDvgdJ0a2y3X+1pMuBaO1TSI0g8M5jG7sQ0viFXtVodtst2anKfSqSrOYFRBPFaIsNVEhl7jylsv2ZfW2+LiRwe/cZ20We9xB+NxNjTnAaZMEosKSUbQdps1BY+UKB6V4e3zC4UxjdnjrM2WPsjMUGVNzllys4qdVrXvokLtJSTDogwBM7PwgeXhAHHdQYSXSVyS6ZUbrwW7IrcPX/ORnTVR/iOETnYrO3y8hudxxtdsMyYT6anhmrNCrt22aUaGjtbkJukqaghNhhftriEy7IDxD+Hd+KvXkktGtYrrwRoiQwGHeAIj4i3zc1F6CN9PXAeE/VGYVVE8JiJ7TgPInI/l3PcAzw1hfQhcJ7vlTPAEOESwzlx35XrxZ5t747CHZUkQZUIcMZRZWnH9NSBbdrwmEUSJT0h9T2H4bxym+F68oNNnlOuTwDYgh6iYusJkqIJrExyP7eEMJZVYgLimEbitpNfkdOZ/xztEdtvjI6662m0hwGxjbF5nPvM4g34zFu/GfVeE/IB1QhT//S0PwuXjQMmAbNlPvgpFkpGEEuIaSihXThKoVdWFUIS4hhLKVZZ21EVCCXENpQrlP7TMlQmxP2I8AAABF3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5HRTwvbWk+PG1vPj08L21vPjxtbj4xNDwvbW4+PG1pPmNtPC9taT48bW8+LDwvbW8+PG1pPkhGPC9taT48bW8+PTwvbW8+PG1uPjEwPC9tbj48bWk+Y208L21pPjxtbz4sPC9tbz48bWk+QUQ8L21pPjxtbz49PC9tbz48bW4+MjQ8L21uPjxtaT5jbTwvbWk+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiZhbXA7PC9taT48bWk+QkM8L21pPjxtbz49PC9tbz48bW4+MTI8L21uPjwvbWF0aD78NlkqAAAAAElFTkSuQmCC)
.
Find the area of the figure.![GE equals 14 cm comma HF equals 10 cm comma AD equals 24 cm straight & BC equals 12](data:image/png;base64,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)
.
![y equals 2 x plus 4](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEoAAAAPCAYAAABDRVmuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAZFJREFUeNpjYKAvsAbiNUD8CYh/AfEFII5mGHzAB4j/D6QDDgJxJBDzQPlaQHwUKjZYAMht1wY6oLABeSC+RCOzyfHsTCBOxqV3LhCHYxEvAOJWOgTWDyxiIMd2YBFvhsrRIqBARcNefHrjgbgLTYwLiG8BsTAOBxDCxAJLaPbDBs4BsTgSPxGIp9AoRbFBU7Y8Pr1eQLwKTaweiGtpnJI4gPgkNCaxAQ8g7oOyXZBimxYBBUq9OYT0glLNFSS+KBDfhXqEVkAQiDcAsRsBdbuB2B5aQwoTETDkpHQ9LKkaZyB/Q2L3QcsnajsIBpSggaRCRIAWQJsSejQszE9icQtOvYehHlCCpiYmGqUkDSCeDS0DiW139ZHZhPhPgjqiI30hEPsB8VIgjqVRIIlDy0IWItSCImwTNEBBbZszRGQ9ajQPCOotgDYTLtGwXNoCTVGEAKiM3IYWMKDW8uLBEFABUEk/GgYUMckbVE2vA2JpLPqXQ2tCegCcAQUKoOMMo4Ag2AZt/I0CPEAHWn6MAhwAAJK9dlmEyKZ8AAAAe3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT55PC9taT48bW8+PTwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjQ8L21uPjwvbWF0aD4tBSpkAAAAAElFTkSuQmCC)
![y equals left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAAARCAYAAAASarh9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAntJREFUeNrtmdFnHEEcx1fUiriXOHEPeQinDxEVIU8n4oSIqjonREREVYmIU/kHqg8RTh5OHvJWeaiqUhURESEi4lSEqKo+VKn8D3mIc0L63fUNazJzO5fdmV3nvny43Z27/e78dn7zmznHSUaroOqkV1V67FT/VjQKzp306zu9dpp/qwbGErz/FDgEN6AB/oItkBXajYN6Cv1PgG/gGjTBT7Aoaafyb0Vj7KgkdQpmgSv4OpK0rbPD0uT/DCyADI9H6GlBw781bYJKSlPdteTcW2EuNun/LsJ3h8AvDf/ODpiXNFwDGzE+jDdqJiXn3yiKm3VeM608+CM5XwAnlvzfRXyGhoZ/5xXf1qD6OH9lFabCUI0aV3HtB8gFjl+DbcMBzvE+3nO+kFx3hZFu0n+UQBcUU4ro33/Ir0Kj9+BdzB172+Lac1Dj52nxTTSQJoOstWjbtOT/sYHuBRcs0sL8+6P2d+B4APzjj9gKtKdjUGQlmW0zWLpZJah+UGZHFSMGOin/e2BG80X1dRP4XAt5y02k7vuaoJnA+i/DYEdJ3VH9tzui8wzy0xZtXFmRWeeX8xzNPQY69LhFirlfH9YUSwXT0ilmTPpvJ9DD4APrqLC5+8EU8hGUwGewZHl55b1c+zTuja5LjdQXp0ZZkImqCEWqSf+6gc6xnnqi0bYiKbL9tLOjWI+Z3DAZ4E5VsGNegk8GNxzm2FE93Cm74srjMRsmcfnXDfQBR7SOpBsmZd6sZHj0nAfmMG8O2QWDknZfWMnGrUl2VoOcMjCiVFuISfvXrYuUW6Alx85mffdPjWT9++mnYMnEipPuv/m8eW25E/0/YzrrqkP1H3m2zB8IZDtmAAAAvnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT55PC9taT48bW8+PTwvbW8+PG1vPig8L21vPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4zPC9tbj48bW8+KTwvbW8+PG1vPig8L21vPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjI8L21uPjxtbz4pPC9tbz48L21hdGg+jErlxgAAAABJRU5ErkJggg==)
The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?
Note:
We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving
by middle term factorisation, we could also use the quadratic formula, which is given by
Where the standard form of equation is
![y equals 2 x plus 4](data:image/png;base64,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)
![y equals left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis](data:image/png;base64,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)
The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?
Note:
We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving
by middle term factorisation, we could also use the quadratic formula, which is given by
Where the standard form of equation is