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Q.

A completes half as much work as B and C completes half as much work as A and B together, at the same time. If C alone can complete the work in 40 days, all of them can together finish the work in:


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a

https://lh4.googleusercontent.com/QJCj_Q6-rCWTgLSGIHe_hlYGS5bOhSGI-W62NDD4XMQOSFcs2yVJOuFE9sFQekKkKWWvk0W67LMxW8HDVnfo4KS_9nM_WZA1xb1XN6jM7-fyA8naXIib5AZ1HEMj7X_Lpic0GTnMKywg96GVseGPwQ

b

https://lh4.googleusercontent.com/yWY3EeIE4_mu4KcgMZUVJTDixDM1H7RS9gp6NdkkjNVoIuWCVgt07I4B9hkpam2REo5CC1Fc4BFGo4iO3HvWxD06S9J9qZP3JVd6pT0hFn1Fd06IVn12K1UzSZREnNQZ0hmc0cr37QT-ZcBozE0qbQ

c

https://lh3.googleusercontent.com/lcY40aid76t02LzbQ-QvuKSlrS0sxwkHq1KHx9klgZLFrNItZrsN0skigqPtEJ3zGzzfW-dMZMGX2D5yp-RnR6a2GgHIYhiyH1WYD91HfCrrfWSF2Ku8OdGiFlIJlQ8XCja1y3mzzDtAF-psXUpzBQ

d

https://lh5.googleusercontent.com/sZe1LygTFTlZShMbHi2O1rzUXkiloGkDGmkz6J16WhwqFiixs0nw4m_qgNwvyTpGadq14I0REGCBfvfGD5zp6mpz53o1qgU417il3f8C72M5utMuryBaUA6FuaoI7-rzSuGZRcyuXjkcMFeAEvDQHg 

answer is A.

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Detailed Solution

Concept- Let us assume that B completes the work in x days. It is given that A completes half as much work as B and C completes half as much work as A and B together. With these relations we can get equations to find the number of days required by each to complete the work individually.
Then we need to add to get the days required to complete the work together by three of them.
If B can complete the work in https://lh4.googleusercontent.com/O2_n3fpT3GvUiOJAuwYhn_3TdKcOO1-p3AYWyLbFMPiqnMVfovpM_Xbo_6hDm52BjJpHWoI95DTxvRyL3nU1d6gWO6klh6nkFPZogD91DejAJPJHnWUAf_JsATChZ18263RDqoGQgSTanQMBUwzl2g, then A can complete the work inhttps://lh6.googleusercontent.com/MrMYP79RZQceKhD88oShCf6U2UVP_1iu8rjjHc3I0QJMpdI9w3Q2e0ljmYa7vZ6noJubb_JqyAZ7xqn2gu1ibLqK4Fb74Ebj2-dMFjdWQ1jhf32ArYC8KMMO8db_C4hSh7HyvX7hK0vtf9gRV05Vqg.
In one day B does work = https://lh4.googleusercontent.com/JcfvVvkSG-luNvXggD3ghZi1E3mHCJO5XS6JOIJ1fvx3pj3CC28BoiISlvtM080vPpIzS3MQade9rn6_PeKiiPrkhjVlhwGURI2vzqsNsmYllMPEHcxCHKhD8KjBGguXpIPA_n_2wNPzxqC2C6HvpQIn one day A does work = https://lh5.googleusercontent.com/v9OkxPfjc2JqgTIgQqtVyZ9Gg8oV_CUbKEuiPKw7mICU83LipxaXhtRRl7ghxDtQRUtWtTih7ijMu-IT04azMY8DuAiyVINmUfObbnZRWK98CvwghPvrL1bGJD8-Jxy9sE6REmMeNulW1k1azfuouwIn one day A and B together do work = https://lh3.googleusercontent.com/AycTGX_ki5vffZiL3L3wXDcwWX99dgwC821cvwHfxwzN6P3Hx0S2aJOIBnwZ0cdGZSL6VTj7Hi-Gw_2hiHko67Gptxj7asMXT02YI2WTWMxS2ODoUCPMn_SotzMX0vK5aT94UQsZnrBy0mN7iihfCwhttps://lh4.googleusercontent.com/ME2nnK5Gd74Gyr69akDAww5sb7eNkQvN1PqyMOgVhwbI9tDEzkLLa92MqSoPjx38JRiRb8kvLfUisFuCWOSPPMkG0H-Nb6Sy78R-dTAHfCsiVWl4hEOeWnw1onbJ1qGmB_UvNc4_UGGXAIjLvLHz0wwork is done by A and B together in one day.
C takes half as much time required by A and B together.
Time taken by C = https://lh4.googleusercontent.com/-t23YQhaDgpRXnscxg7g8w2oDb0V94qc8JVs-wuLN-qPxzpllztL7gNK-mVCUAC323gRnK_LVEYLV9ZZfPNcJcFraAM65mU1oesz6dcQCVrfYjEMGG-CjnOvudxs-xvGl6xgPpCJ8bzyI7fLujWRZghttps://lh3.googleusercontent.com/DzFoEEpHvHcFnpdK16jqzxFAbIUwuP87CQH81D25jabEvq8Hej1uW6oEJMDdphFIakJs_rlISoTshA58yaMI8IDVza2s3MSZv2NG5jFtfUkxWrVgtkLv-AmFpGFLTcBVD6YfCqYFnWbCrCH3tjPgVAA, B, C can work together in one day = https://lh5.googleusercontent.com/NKh77EnQyVRQsYfRZC9TgYYBE2s6KvjUHDYlRHsMNwhHCs4TwURSs5UWmQApggjDmorw0v0hmOrRtqyTS94V7E2BM4Hhb4bM21EOhMccwyf77PDw4iXC_1kWVpUY5cSkQhF8B1_Aog06OLY6RxrtcAA, B, C can complete the work together in= https://lh4.googleusercontent.com/cRzrVvg158zv9_jdaw7psrV_QBvt3CLblQcVKvfeBbtT1xjHxE1-Ao33rdk_uaEs0Ui3mYElCD3zX43pG-T8TPBPyi6tQEK2TP43MQlxDAfLyavu_oD-2ocMFNLJSiPsEKUBJGuDdBBVpFysPoAlrQHence, the correct answer is 1) https://lh4.googleusercontent.com/QJCj_Q6-rCWTgLSGIHe_hlYGS5bOhSGI-W62NDD4XMQOSFcs2yVJOuFE9sFQekKkKWWvk0W67LMxW8HDVnfo4KS_9nM_WZA1xb1XN6jM7-fyA8naXIib5AZ1HEMj7X_Lpic0GTnMKywg96GVseGPwQ 
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